83 free MCQs on Oscillations, each with its own worked answer and explanation. Simple harmonic motion, spring-mass, pendulum, energy in SHM, and resonance.
Take the timed Oscillations chapterwise test →83 practice questions on Oscillations, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Oscillations notes.
In SHM, displacement and velocity are 90° out of phase (v is maximum when x=0, and zero when x is extreme), while acceleration is always exactly opposite in sign to displacement, consistent with a = −ω²x.
Q1.
In simple harmonic motion, the acceleration of the particle is maximum at:
Q2.
The projection of a particle in uniform circular motion onto a diameter executes:
Q3.
The SI unit of angular frequency ω is:
Q4.
The graph of restoring force versus displacement for a body in SHM is:
Q5.
In simple harmonic motion, the restoring force is:
Q6.
The time period of a simple pendulum of length L is:
Q7.
The time period of a spring-mass system with spring constant k and mass m is:
Q8.
At the equilibrium position of a body in SHM:
Q9.
The angular frequency ω of SHM is related to frequency f by:
Q10.
In SHM, the total mechanical energy is:
Q11.
A seconds pendulum has a time period of:
Q12.
The displacement of a body in SHM is given by x = A sin(ωt + φ). The amplitude A represents:
Q13.
When the amplitude of oscillation is doubled, the total energy of SHM:
Q14.
Which of the following is NOT an example of simple harmonic motion?
Q15.
The phase difference between displacement and velocity in SHM is:
Q16.
Resonance occurs when the driving frequency equals:
Q17.
A spring of spring constant k is cut into two equal halves. Each half has spring constant:
Q18.
The equation of SHM a = -ω²x implies:
Q19.
A pendulum clock is taken to the Moon (g<sub>moon</sub> = g/6). Its period becomes:
Q20.
In damped oscillation, the amplitude:
Q21.
Two springs with constants k<sub>1</sub> and k<sub>2</sub> are connected in parallel supporting a mass m. The effective spring constant is:
Q22.
The velocity of a particle in SHM at displacement x from equilibrium (amplitude A) is:
Q23.
A spring-mass system oscillates vertically. If mass is increased 4 times, the time period:
Q24.
The kinetic energy of a particle in SHM is maximum at:
Q25.
A particle executes SHM of amplitude 8 cm with a period of 0.5 s. Its maximum acceleration is about:
Q26.
A particle in SHM has displacement x = 4 sin(2πt) cm. Its maximum speed is:
Q27.
In SHM the potential energy equals one-fourth of the total energy at displacement:
Q28.
A 0.2 kg mass on a spring of force constant 80 N/m oscillates in SHM. Its frequency is about:
Q29.
A particle in SHM has period 1.2 s. The time taken to move from the mean position to half the amplitude is:
Q30.
A spring of spring constant 200 N/m has a mass of 0.5 kg. What is the time period of oscillation?
Q31.
Two identical springs each with k = 50 N/m are connected in series. A mass of 2 kg oscillates on this combination. What is T?
Q32.
In SHM, when the displacement is half the amplitude, what fraction of total energy is kinetic?
Q33.
The potential energy of a spring-mass system executing SHM is (1/2)kx². If x = A sin(ωt), then PE averaged over a full cycle is:
Q34.
A physical pendulum (rigid body) has MI I about pivot and its CM is at distance d. Its time period is:
Q35.
A mass is attached to two springs of constants k<sub>1</sub> and k<sub>2</sub> in series. If k<sub>1</sub> = k<sub>2</sub> = k, the effective constant is:
Q36.
A particle performs SHM with amplitude 0.1 m and frequency 5 Hz. What is its maximum velocity?
Q37.
The displacement x = 5 sin(10t + π/6) cm. What is the initial phase?
Q38.
The restoring torque on a simple pendulum of mass m and length L displaced by small angle θ is:
Q39.
For a spring-mass system, the time period in a lift accelerating upward with acceleration a is:
Q40.
A tuning fork of frequency 256 Hz produces SHM. What is the period?
Q41.
In forced oscillations with damping, the steady state amplitude is maximum when:
Q42.
A horizontal spring-mass system executes SHM. If the spring is replaced with one that is 4 times stiffer, the period:
Q43.
A particle oscillates between x = -5 cm and x = +5 cm. Its amplitude and equilibrium position are:
Q44.
The time period of oscillation of a liquid in a U-tube of total length L (liquid length) is:
Q45.
The equation x = 3 sin(πt) + 4 cos(πt) represents SHM. What is the amplitude?
Q46.
The acceleration of a SHM particle at displacement x is a = -36x m/s². What is the time period?
Q47.
A spring stretches by 0.2 m when a mass of 2 kg is hung from it. The time period of vertical oscillation is:
Q48.
In SHM, the kinetic and potential energies are equal when:
Q49.
The Q factor (quality factor) of an oscillator measures:
Q50.
A spring of force constant 12 N/m is cut into three equal parts and all three parts are joined in parallel to support a block. The effective force constant is:
Q51.
Two springs of constants 100 N/m and 200 N/m are joined in series and carry a 3 kg mass. The time period of SHM is about:
Q52.
A particle in SHM of amplitude 10 cm has a speed of 8 cm/s when its displacement is 6 cm. Its time period is:
Q53.
A uniform rod of length 1.5 m is pivoted at one end and swings as a physical pendulum (I = mL<sup>2</sup>/3, centre of mass at L/2). Taking g = 10 m/s<sup>2</sup>, its time period is:
Q54.
The amplitude of a damped oscillator falls to one-third of its initial value in 10 s. After 20 s from the start its amplitude will be:
Q55.
A block of mass m on a spring of constant k executes SHM of amplitude A. As it passes the mean position an equal mass m is gently placed on it and sticks. The new amplitude is:
Q56.
A particle executes SHM with amplitude A. At time t=0, x = A/2 and velocity is positive. The phase constant φ in x = A sin(ωt + φ) is:
Q57.
Two SHMs x<sub>1</sub> = A sin(ωt) and x<sub>2</sub> = A sin(ωt + π/3) are superposed. The amplitude of the resultant is:
Q58.
A mass m is connected to two springs (k<sub>1</sub> = k, k<sub>2</sub> = 3k) in parallel. If one spring is cut, what is the ratio of new period to original?
Q59.
A pendulum of length L on a trolley that accelerates at a (horizontal) has effective gravity g<sub>eff</sub> = √(g²+a²). Its period is:
Q60.
For a spring-mass system, if the amplitude is halved by damping, the energy becomes:
Q61.
A horizontal disk oscillates as a torsional pendulum. If the wire has torsional constant k<sub>T</sub> and the disk has MI I, the period is:
Q62.
A particle of mass m is in SHM. At time t, its displacement is x = a cos(ωt). The time it takes to go from x=a to x=a/2 is:
Q63.
In forced oscillations, the phase lag of displacement behind the driving force at resonance is:
Q64.
Two masses m<sub>1</sub> and m<sub>2</sub> are connected by a spring of constant k. The reduced mass is μ = m<sub>1m</sub>_2/(m<sub>1</sub>+m<sub>2</sub>). The angular frequency of oscillation is:
Q65.
The time-averaged potential energy of an SHM particle equals:
Q66.
A particle executes SHM with T = 2 s and amplitude 5 cm. The distance covered by the particle in one full time period starting from extreme is:
Q67.
A block on a spring (k = 200 N/m) is given an initial displacement of 5 cm and initial velocity of 1 m/s. The amplitude of oscillation (mass = 2 kg) is:
Q68.
A tunnel is drilled through the Earth along a diameter. A ball dropped in undergoes SHM with period:
Q69.
The equation x = A e<sup>-bt/2m</sup> sin(ω_d t + φ) describes:
Q70.
At what position in SHM is the KE equal to twice the PE?
Q71.
Two springs k<sub>1</sub> and k<sub>2</sub> are attached to a block between two walls. The block is displaced and released. The effective spring constant is:
Q72.
A simple pendulum of length L is executing SHM. The tension in the string at the lowest point when the bob has speed v is:
Q73.
The quality factor Q of a damped oscillator with natural frequency f<sub>0</sub> = 1000 Hz and bandwidth Δf = 10 Hz is:
Q74.
For a seconds pendulum on Earth (T = 2 s, L = 1 m), what must be the length on a planet where g = 4 m/s² for the same period?
Q75.
In the equation of SHM, x = 10 sin(πt/2) cm. The acceleration when x = 6 cm is:
Q76.
A particle in SHM has amplitude 5 cm and period 2 s. Its maximum speed is:
Q77.
The length of a simple pendulum is increased to 4 times its original value. Its period becomes:
Q78.
Two identical springs each of constant k are connected in parallel and support a mass m. The period of oscillation is:
Q79.
For a particle in SHM, at displacement x = A/2 the ratio of its kinetic energy to potential energy is:
Q80.
A particle in SHM has angular frequency 10 rad/s and amplitude 0.1 m. Its maximum acceleration is:
Q81.
When a simple pendulum is in a lift that accelerates upward with acceleration a, its period:
Q82.
At the mean (equilibrium) position of a particle executing SHM:
Q83.
A mass on a spring has period T. If the mass is quadrupled, the new period is:
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