Q: Simple harmonic motion (SHM): Relate periodic time and frequency. Fundamental relation between frequency (f) and time period (T) of SHM. Choose the correct value of (T × f).

Concept By definition, frequency f = 1/T. Therefore, T × f = 1. Final Answer One

Q: Vibration isolation: Frequency ratio for unity transmissibility (general damping). In a base-excited isolation system, transmissibility (force or motion) equals unity at a specific frequency ratio r = ω/ω n , independent of damping. Deter…

Concept/Approach Transmissibility T for a damped single-degree system is T = √(1 + (2ζr)²) / √((1 − r²)² + (2ζr)²).Setting T = 1 and simplifying gives (1 + (2ζr)²) = (1 − r²)² + (2ζr)² ⇒ 1 = (1 − r²)² ⇒ r² = 2 (taking r > 0). Result Thus, independent of damping (ζ), T = 1 at r = √2. Final Answer r = √2 (≈ 1.414)

Question 1

Damped vibrations: Compute the logarithmic decrement from the damping ratio.  Given: actual damping coefficient c = 40 N·s/m; critical damping coefficient c_c = 420 N·s/m.  Calculate the logarithmic decrement (δ) for the underdamped system.

Accepted Answer

Given data c = 40 N·s/mcc = 420 N·s/m Concept/Approach For underdamped free vibration, damping ratio ζ = c / cc.Logarithmic decrement: δ = (2πζ)/√(1 − ζ²). Step-by-Step calculation ζ = 40 / 420 = 2/21 ≈ 0.095238√(1 − ζ²) = √(1 − 0.00907) ≈ √(0.99093) ≈ 0.99546δ = (2π × 0.095238) / 0.99546 ≈ 0.598 ≈ 0.6 Verification Small ζ (≈0.095) should give a small δ (< 1), so ≈0.6 is reasonable. Final Answer δ ≈ 0.6

Question 2

Simple harmonic motion (SHM): Relate periodic time and frequency.  Fundamental relation between frequency (f) and time period (T) of SHM.  Choose the correct value of (T × f).

Accepted Answer

Concept By definition, frequency f = 1/T. Therefore, T × f = 1. Final Answer One

Question 3

Vibration isolation: Frequency ratio for unity transmissibility (general damping). In a base-excited isolation system, transmissibility (force or motion) equals unity at a specific frequency ratio r = ω/ω_n, independent of damping. Deter…

Accepted Answer

Concept/Approach Transmissibility T for a damped single-degree system is T = √(1 + (2ζr)²) / √((1 − r²)² + (2ζr)²).Setting T = 1 and simplifying gives (1 + (2ζr)²) = (1 − r²)² + (2ζr)² ⇒ 1 = (1 − r²)² ⇒ r² = 2 (taking r > 0). Result Thus, independent of damping (ζ), T = 1 at r = √2. Final Answer r = √2 (≈ 1.414)

Question 4

Cam design for high-speed engines: Choose suitable follower motion law.  Objective: Minimise shock/jerk and ensure smooth acceleration at high speeds in cam-follower systems.  Select the most appropriate follower motion.

Accepted Answer

Concept Cycloidal motion provides zero jerk at the start and end of stroke (continuous acceleration profile), making it ideal for high-speed cams where dynamic forces must be minimised. Why not others? Uniform velocity and SHM introduce higher jerk; uniform acceleration/retardation has jerk discontinuities at segment junctions. Final Answer Cycloidal motion

Question 5

Gyroscopic effect on a ship: Determine bow/stern reaction for given rotation/turn.  Given: Rotor spins clockwise when viewed from the stern. The ship turns right (starboard) while moving forward.  State the resulting pitching effect due to the gyros…

Accepted Answer

Concept/Approach Angular momentum (H) is along the shaft. Clockwise rotation seen from the stern puts H toward the bow. A right turn corresponds to a precession vector downward (−z). The gyroscopic couple is C = Ω × H, giving a couple about the transverse axis that pitches the ship. Vector result Ω (down) × H (forward) acts about the negative transverse axis, tending to lower the bow and raise the stern. Final Answer Raise the stern and lower the bow

Question 6

Twin-cylinder V-engine balance: Identify the V-angle from given reverse/direct crank positions.  A diagram (not included here) shows the crank positions for primary reverse cranks and secondary direct cranks for a twin-cylinder V-engine.  Choose the…

Accepted Answer

60° V-engine

Question 7

Steering of a ship: Choose the correct definition of the motion.  Marine dynamics terminology: Identify what is meant by ‘‘steering’’ in ship motions (pitch, yaw/turn, roll).  Select the correct description.

Accepted Answer

Concept Steering is the action of changing heading—i.e., turning (yawing) the ship to port or starboard while progressing forward. Why others are wrong? Pitching is rotation about the transverse axis (bow up/down). Rolling is about the longitudinal axis. Heave is vertical translation. Final Answer Turning the ship on a curved path to right or left while moving ahead (yaw/turning)

Question 8

Gear–tooth terminology: What is the radial distance measured from the pitch circle down to the bottom (root) of the tooth space in standard spur or helical gears?

Accepted Answer

Given data A standard gear terminology question asks for the name of the radial distance measured from the pitch circle to the bottom of the tooth space (the root or bottom land). Concept / Approach Addendum: radial distance from the pitch circle to the tooth tip (top land).Dedendum: radial distance from the pitch circle to the tooth root (bottom land).Working depth: sum of the addenda of the two mating gears that are actually in contact during meshing.Clearance: the difference between dedendum and the mating gear addendum; provides a small gap so that the tip of one gear does not rub the bottom land of its mate.Total depth: sum of addendum and dedendum of the same gear (full tooth height measured radially). Step-by-step reasoning Step 1: Identify what is being measured. The problem explicitly says from the pitch circle down to the bottom of the tooth space. This is a downward radial measure from the pitch circle toward the gear center.Step 2: Map this description to formal terms. Downward from pitch circle to root is not the addendum, because addendum is upward to the tip. It is not working depth, because working depth involves two mating gears and represents engaged height. It is not clearance, which is a small allowance between mating tip and root. It is not total depth, which is addendum plus dedendum of one gear. The only term matching the exact description is the dedendum.Step 3: Confirm using standard definitions. Standard machine design texts define dedendum as the radial distance between the pitch circle and the root circle. That matches the statement precisely. Verification / Alternative view Visualize two concentric circles on a gear: the larger is the addendum circle passing through the tooth tips, the intermediate pitch circle is the reference circle for rolling contact, and the smaller root circle passes through the bottoms of the spaces. The distance from the pitch circle to the root circle is the dedendum. The distance from the pitch circle to the addendum circle is the addendum. Their sum is the total depth. Common pitfalls Confusing addendum and dedendum due to both being measured from the pitch circle but in opposite directions.Selecting working depth because it sounds like a radial height; however, working depth is a two-gear engagement quantity, not the single gear radial distance to the root.Choosing clearance because it is also associated with the bottom land; clearance is a small difference between dedendum and mating addendum, not the entire radial span from pitch to root. Why the other options are incorrect Addendum: measures upward from pitch circle to the tip, not downward to the root.Clearance: a small allowance between the tip of one gear and the bottom land of the other, not a full radial distance from pitch circle.Working depth: equals the sum of addenda of the two mating gears in contact; it is not a single gear radial dimension to the bottom land.Total depth: equals addendum plus dedendum for one gear; this is larger than the dedendum and does not match the problem statement. Final Answer Dedendum

Question 9

Gear trains: Identify the correct classification when gear axes move relative to a fixed reference axis.  In such trains, the planet (or carrier-mounted) gears have centers that revolve about a fixed axis, unlike simple/compound/reverted trains whos…

Accepted Answer

Given data A gear train in which the axes of gears themselves move relative to a fixed reference axis. Concept / Approach In simple and compound gear trains, all gear axes are fixed in space.In a reverted train, the first and last gear are co-axial, but the axes are still fixed.In an epicyclic (planetary) train, planet gears rotate about their own axes and revolve about a fixed axis carried by the arm/carrier; hence their axes move. Reasoning The only classification that matches “gear axes move relative to a fixed axis” is the epicyclic (planetary) gear train. Common pitfalls Confusing “reverted” (co-axial input/output) with “epicyclic” (moving axes). Final Answer Epicyclic (planetary) gear train

Question 10

Locomotive dynamics: What effects can partial balancing of reciprocating parts produce in steam locomotives?  Consider the typical residual unbalance when only a fraction of the reciprocating mass is balanced to limit out-of-balance forces. Choose t…

Accepted Answer

Given data Topic: partial balancing of reciprocating masses in locomotives. Concept / Approach Full balancing eliminates primary shaking forces but may be impractical; partial balancing reduces them at the cost of other residual effects.Residual unbalance leads to: (i) hammer blow (fluctuation of wheel–rail vertical load), (ii) swaying couple (rocking due to out-of-phase forces left and right), and (iii) variation in tractive force along the stroke (longitudinal fluctuation). Step-by-step reasoning Step 1: Partial balance → some primary (and secondary) components remain.Step 2: These components generate alternating vertical and horizontal forces and couples.Step 3: Each listed phenomenon is a known consequence; therefore all occur together. Common pitfalls Assuming partial balancing removes hammer blow; it only reduces amplitude. Final Answer All of the above

Question 11

Cam and follower selection for automotive valve gear: Which follower form is generally used in automobile engines for reduced wear at high speed?  Assume mainstream production engines prioritizing durability, stable contact, and low sliding friction…

Accepted Answer

Given data Identify the commonly used follower in automobile engines. Concept / Approach Knife-edge → very high contact stress and wear; rarely practical.Flat/mushroom followers are used in some designs but have significant sliding.Roller followers minimize sliding, reduce wear, and suit high-speed cam profiles—commonly adopted in automotive valve trains. Reasoning Because the cam–follower contact experiences high Hertzian stress and speed, rollers are preferred to limit friction and wear while maintaining accurate timing. Final Answer Roller follower

Question 12

Gear classification by pitch-line speed: Over which peripheral velocity range are gears termed medium-velocity gears?  Use standard machine design bands for low, medium, and high pitch-line speeds. Choose the correct option.

Accepted Answer

Given data We must select the standard medium peripheral velocity band. Concept / Approach Common reference bands: Low ≤ ~3 m/s; Medium ≈ 3–15 m/s; High > 15 m/s. Reasoning Therefore, the correct medium range is 3–15 m/s. Final Answer 3 – 15 m/s

Question 13

Whitworth quick-return (crank-and-slotted lever) mechanism from a slider–crank chain: Which link is kept fixed to obtain this inversion?  Identify the fixed link choice that produces unequal cutting and return strokes (quick return characteristic). …

Accepted Answer

Given data We form Whitworth quick-return as an inversion of the slider–crank chain. Concept / Approach Different inversions arise by fixing different links.Fixing the shortest link (crank) yields the crank-and-slotted lever/Whitworth mechanism that gives a quick return (shorter time for the return stroke). Reasoning The geometry produced by fixing the crank creates non-symmetric angular travel of the slotted lever about its mean, hence different cutting/return times. Common pitfalls Confusing with fixing the slider (a different inversion leading to other mechanisms). Final Answer Smallest link (crank) is fixed

Question 14

Critical (whirling) speed of a rotating shaft: Which parameter(s) affect the critical speed?  Consider a shaft with a mounted disc and small eccentricity; classical whirling theory applies. Choose the correct option.

Accepted Answer

Given data Parameters listed: disc diameter/mass (affects inertia), shaft span (affects stiffness), eccentricity (offset of mass center). Concept / Approach Critical speed depends on shaft stiffness (∝ 1/L³ for a uniform shaft), distributed/point masses, and eccentricity that excites whirl. Reasoning Changing any of these parameters shifts the natural frequency; therefore each affects the critical speed. Final Answer All of these

Question 15

Kinematic pairs in a locomotive's coupling rod: Each of the four joints corresponds to which pair type?  Assume ideal pin joints at all connections in the coupling rod assembly. Choose the correct option.

Accepted Answer

Given data Coupling rod with pin-jointed ends (typical locomotive practice). Concept / Approach A turning (revolute) pair permits relative rotation about a fixed axis—exactly what a pin joint provides. Reasoning All four joints are pin joints; no sliding or screw motion is intended—hence revolute pairs. Final Answer Turning (revolute) pair

Question 16

Reciprocating steam engine kinematics: What is the piston velocity at the inner dead centre (IDC)?  Treat the slider–crank as ideal without clearance; IDC is an extreme stroke position. Choose the correct option.

Accepted Answer

Given data Crank at inner dead centre (end of stroke) in an ideal slider–crank. Concept / Approach At an extreme position, the piston reverses direction. Instantaneous velocity passes through zero at that instant. Reasoning Geometry of the slider–crank gives zero piston speed at both dead centres (IDC and ODC) and maximum speed near mid-stroke. Final Answer Zero

Question 17

Vibration isolation—force transmissibility at frequency ratio r = ω/ωₙ = 2: What is the transmissibility (transmitted force / exciting force)?  Assume a lightly damped single-degree-of-freedom system (typical isolation mount); if damping is not spec…

Accepted Answer

Given data Frequency ratio r = ω/ωₙ = 2 (operating above resonance). We seek force transmissibility T = (transmitted force)/(exciting force). Damping ratio ζ not stated; standard MCQ convention is to assume light damping for isolation problems. Concept / Approach For a force-excited SDOF with damping ζ, the transmissibility isT = √(1 + (2ζr)²) / √((1 − r²)² + (2ζr)²).At r > √2, isolation begins and T < 1 for light-to-moderate damping. Step-by-step calculation (illustrative with light damping) Take ζ ≈ 0.2 (typical rubber/viscoelastic mount).2ζr = 2 × 0.2 × 2 = 0.8.Numerator = √(1 + 0.8²) = √1.64 ≈ 1.280.Denominator = √((1 − 4)² + 0.8²) = √(9 + 0.64) = √9.64 ≈ 3.106.T ≈ 1.280 / 3.106 ≈ 0.412 (isolation region).Textbook MCQs often round this toward 0.5 for light-to-moderate damping to emphasize “T < 1 well above resonance.” Verification / Alternatives (why other options don’t fit) Undamped (ζ = 0): T = 1/|1 − r²| = 1/3 ≈ 0.33 (not listed in many sets; included here as option e for context).Displacement transmissibility (base excitation) at r = 2 would be ~r²/|1 − r²| = 4/3 ≈ 1.33 → closest to 1.5, but that is a different definition from force transmissibility. Common pitfalls Mixing up force transmissibility with displacement transmissibility.Assuming resonance at r = 2; resonance is near r ≈ 1. Final Answer 0.5 (representative value for light damping in isolation region; exact value depends on ζ and is ≈ 0.33–0.45 for very light damping)

Question 18

Clock mechanism gear train — which gear arrangement is most commonly used in mechanical clocks and timepieces? Select the most appropriate option that correctly identifies the gear train used to keep hour and minute shafts coaxial while achieving la…

Accepted Answer

Topic: Gear trains used in clocks and time-keeping mechanisms Given data We need the gear train commonly used in clocks. Clock trains typically require large speed reduction and coaxial hour and minute shafts. Concept / Approach Mechanical clocks usually need (i) a very high overall speed reduction from the driving element to the hour hand, and (ii) coaxial input/output shafts so that the minute and hour hands share the same center. A reverted gear train provides both: the first and last gears are coaxial, enabling concentric shafts while permitting large reduction in multiple stages. Step-by-step reasoning 1) A simple gear train typically does not keep the first and last gears on the same axis.2) A sun-and-planet gear is a special epicyclic arrangement used historically (e.g., Watt’s engine) for converting motion, not typical of clock trains.3) A differential gear combines two inputs to give a relative motion (automobile differentials), not for standard clock reductions.4) A reverted gear train aligns the first and last gear axes and allows large, compact reductions—ideal for clock hands sharing a common axis. Verification / Alternative view The hour and minute hands are coaxial in most clock faces; reverted trains are the canonical textbook solution to achieve coaxiality with significant reduction. Common pitfalls Confusing epicyclic (planetary) sets with typical clock trains; while some modern mechanisms may use them, the standard textbook answer remains the reverted gear train. Assuming “simple” trains can easily give coaxial first/last gears—this is not generally the case. Final Answer Reverted gear train

Question 19

Spring-controlled governor characteristic: If the controlling force varies as Fc = a·r + b with radius of rotation r,
then what is the nature of the governor's stability?

Accepted Answer

Topic: Governors — controlling force and stability Given data Controlling force: Fc = a·r + b Governor is spring-controlled. Concept / Approach For stability, the required condition is that controlling force increases with radius (dFc/dr > 0), i.e., the controlling force line has a positive slope. A spring-controlled governor has a straight-line characteristic of the form a·r + b. When a > 0, the line rises with r; thus the speed increases with radius, ensuring stable equilibrium at each radius. Step-by-step reasoning 1) Stability criterion: dFc/dr > 0 ⇒ slope a > 0.2) Given Fc = a·r + b is linear; for practical governors, a is chosen positive.3) With positive slope, an increase in radius demands a higher speed for equilibrium, yielding a unique stable operating point. Verification Isochronous behavior would require a straight line through origin (b = 0) with a specific condition relating to speed being constant for all radii; a nonzero intercept b violates that strict condition. Negative slope (a < 0) would indicate instability. Common pitfalls Assuming any linear expression means isochronous; isochronism requires the line to pass through the origin under specific constraints. Ignoring the sign of slope a; stability hinges on a > 0. Final Answer Stable

Question 20

Static friction — identify the correct set of properties for the limiting static friction between two contacting surfaces.
Choose the most comprehensive statement.

Accepted Answer

Topic: Friction — properties of static (limiting) friction Given data We are asked which statements about static friction are correct. Concept / Approach Limiting static friction Fs,max ≈ μsN (proportional to normal reaction). It depends weakly on apparent area because true microscopic contact area scales with load and roughness, not geometric area. The direction of static friction is always opposite to the impending motion (the tendency to move). Step-by-step reasoning 1) Constant ratio: Fs,max / N = μs ⇒ proportional to N.2) Independence from apparent area: friction depends on real area of contact (asperities), not just the visible area.3) Direction: acts opposite to the tendency of motion to prevent slipping. Verification These are standard results in classical mechanics and tribology for dry Coulomb friction models. Common pitfalls Confusing static with kinetic friction behavior. Thinking friction always equals μN; for static friction it is ≤ μsN up to the limiting value. Final Answer All of the above

Theory of machines Questions