Oscillations — Previous-Year Questions

Q1. Period of SHM with k = 100 N/m and m = 0.25 kg:

Q2. If amplitude is doubled, period of SHM:

Q3. SHM equation x = 5·sin(2t + π/4). Angular frequency:

Q4. Acceleration in SHM is:

Q5. If a particle has x = 3sin(ωt) + 4cos(ωt), its amplitude:

Q1. If x = 4·cos(2t + π/3), the amplitude and angular frequency:

Q2. Particle in SHM crosses equilibrium with v = 6 m/s, amplitude 0.5 m. Angular frequency:

Q3. Time-average of x over one full SHM period:

Q4. If x = 5·sin(πt), how far does the particle travel in one full period?

Q5. Two SHMs of equal A and ω are 90° out of phase. Their superposition:

Q1. SHM amplitude 0.2 m, ω = 5 rad/s. Maximum velocity:

Q2. Velocity of a particle in SHM at x = A/2:

Q3. Phase difference between v(t) and x(t) in SHM:

Q4. Where is KE maximum in SHM?

Q5. If x = 5cos(2t) m, instantaneous velocity at t = π/8 s:

Q1. SHM amplitude 0.1 m, ω = 10 rad/s. Maximum acceleration:

Q2. In SHM, acceleration is MAXIMUM:

Q3. Equation x = 2cos(πt) m, acceleration at t = 1 s:

Q4. Force on a 0.5 kg mass in SHM with k = 200 N/m at x = 0.1 m:

Q5. An a-x graph for SHM is:

Q1. Mass 0.5 kg on a spring of k = 50 N/m. Period:

Q2. If m is doubled (k unchanged), period:

Q3. A horizontal spring-mass at amplitude A = 0.05 m, k = 100 N/m. Max KE:

Q4. For a vertical spring-mass system, gravity:

Q5. Two springs k = 50 N/m each in PARALLEL with one mass m. Effective k:

Q1. A 0.2 kg mass stretches a spring by 5 cm. Period of vertical oscillation:

Q2. Does gravity change the period of a vertical spring-mass system?

Q3. Static extension δ of a vertical spring with mass m and constant k is:

Q4. Vertical spring with δ = 0.04 m. Frequency of small oscillations (g = 10):

Q5. In a vertical spring at the new equilibrium, the spring force is:

Q1. A spring (k = 200 N/m) of amplitude 0.1 m. Total energy:

Q2. If amplitude is doubled, total energy:

Q3. KE equals PE in SHM when x equals:

Q4. Time-average of KE over one period of SHM = total energy ×:

Q5. If a particle in SHM has total energy 5 J and at some instant KE = 2 J, the PE is:

Q1. Spring-mass: m = 0.5 kg, T = 0.3 s. If m doubled, new T:

Q2. Period of simple pendulum DOES depend on:

Q3. Plot of T² vs m for spring-mass is:

Q4. Spring constant k = 100 N/m. Mass for T = 1 s:

Q5. Pendulum: if you replace lead bob with lighter aluminum bob (same shape and size):

Q1. Spring: m = 0.5 kg, k = 200 N/m. Period:

Q2. If k is doubled (m same), T becomes:

Q3. Two springs k = 50 each in SERIES with mass m. Effective k:

Q4. If we want to halve T of a spring-mass, we need k to be:

Q5. Springs in PARALLEL combined behave like a:

Q1. A simple pendulum of length 1 m. Period (g = 9.8 m/s²):

Q2. If pendulum length is doubled, period changes by factor:

Q3. Period of a simple pendulum depends on:

Q4. Pendulum that beats seconds (T = 2 s) on Earth — its length:

Q5. Same pendulum on the Moon (g = 1.6 m/s²) has period:

Q1. Pendulum length 100 cm. Period (g = 9.8 m/s²):

Q2. If pendulum length is quadrupled, period:

Q3. Slope of T² vs L graph for a simple pendulum equals:

Q4. Length L for a 1-second pendulum (T = 1 s):

Q5. Why is pendulum L measured to bob's CENTER OF MASS?

Q1. Same pendulum on Earth (g = 9.8) and Moon (g = 1.6). Ratio T_moon / T_earth:

Q2. If g doubles, pendulum period:

Q3. Pendulum at the top of a tall mountain runs:

Q4. g measurement gives 4π²L/T². If L = 1 m, T = 2 s, g equals:

Q5. Why does pendulum clock period change with location on Earth?

Q1. Underdamped oscillator's amplitude:

Q2. Critically damped system:

Q3. If b = 0 (no damping), motion is:

Q4. Q-factor measures:

Q5. Shock absorbers in vehicles are typically:

Q1. Steady-state amplitude is MAXIMUM when:

Q2. At resonance, phase between drive and response is:

Q3. Forced oscillator at steady state has frequency:

Q4. If damping is reduced, the resonance peak becomes:

Q5. Tacoma Narrows Bridge collapse (1940) is a famous example of:

Q1. At resonance in a damped forced oscillator:

Q2. Q-factor of an oscillator measures:

Q3. What happens to A_res if damping b is doubled?

Q4. Tacoma Narrows Bridge collapsed in 1940 because:

Q5. Soldiers BREAK STEP when crossing a bridge to: