This page covers CAPF AC Oscillations with complete concept notes, 18 graded practice MCQs, key points and exam-specific tips. Free to study.
18graded MCQs · easy to hard · full solution & trap analysis
The equation of oscillation of a particle is x = 8 sin(5t) cm, where t is in seconds. What is the frequency of oscillation?
A simple pendulum of length 1 m oscillates with a time period of 2 seconds. What is the acceleration due to gravity at that location? (Use π² ≈ 10)
A mass-spring system oscillates with amplitude 5 cm and angular frequency 10 rad/s. What is the maximum velocity of the mass?
A particle undergoes simple harmonic motion with time period T = 4 seconds. At t = 0, it is at the mean position. How much time will it take to reach the maximum displacement for the first time?
A pendulum bob of mass 200 g oscillates with amplitude 10 cm. If the time period is 2 seconds, what is the maximum kinetic energy of the bob? (Use π² ≈ 10)
A pendulum swings with maximum velocity 2 m/s and amplitude 0.2 m. What is its angular frequency?
Two identical springs with spring constant k = 100 N/m are connected in series. A mass of 2 kg is attached. What is the time period of oscillation?
A body oscillates with SHM. When its displacement is 3 m, velocity is 4 m/s, and when displacement is 4 m, velocity is 3 m/s. What is the amplitude?
The total energy of a harmonic oscillator is 200 J. If the amplitude is 0.4 m, what is the spring constant?
A particle undergoes SHM with time period 4 s. Starting from equilibrium, how much time will it take to reach half the amplitude?
A simple pendulum of length 1 m oscillates with a time period of 2 seconds. If the length is increased to 4 m, what will be the new time period?
A mass of 0.5 kg undergoes simple harmonic motion with amplitude 2 m and angular frequency 5 rad/s. What is the maximum kinetic energy?
The equation of a wave is y = 0.04 sin(100t + 2x) meters. What is the frequency of oscillation?
A particle in SHM has displacement x = 3 cos(4t) cm. What is the maximum acceleration?
A particle in SHM has period T = 4 s and amplitude A = 0.5 m. If the particle starts from mean position, the distance travelled in time t = 1 s is:
The kinetic and potential energies of a particle executing SHM are equal at a certain instant. The displacement of the particle at this moment is (take amplitude = A)
A mass-spring system undergoes simple harmonic motion with amplitude A = 0.2 m and angular frequency ω = 10 rad/s. What is the maximum velocity of the oscillating mass?
A simple pendulum of length 1 m oscillates with a time period T₁. When the length is increased to 4 m, the new time period T₂ becomes how many times T₁?