Oscillations

A particle executes SHM with a frequency of 5 Hz. What is its time period?

A particle executes SHM with amplitude 0.04 m and angular frequency 10 rad/s. What is the maximum speed of the particle?

A particle in SHM has amplitude 5 cm and angular frequency 2 rad/s. What is its speed when its displacement from the mean position is 3 cm?

A particle executes SHM with amplitude 0.02 m and angular frequency 50 rad/s. What is its maximum acceleration?

A block of mass 0.5 kg is attached to a spring of force constant 200 N/m. What is the time period of its oscillation?

A spring of force constant k, loaded with mass m, has time period T. The spring is now cut into two equal halves, and the same mass m is attached to just one half. What is the new time period, in terms of T?

Two springs of force constants 200 N/m and 300 N/m are connected in series. What is the effective spring constant of the combination?

Using g ≈ π² m/s², what is the time period of a simple pendulum of length 1 m? (This is essentially the principle behind the second's pendulum used to define standard timekeeping.)

A simple pendulum has time period T when hanging at rest in a lift. If the lift accelerates upward with acceleration equal to g, what is the new time period in terms of T?

The length of a simple pendulum is increased by 21%. What is the percentage change in its time period?

If the amplitude of a particle executing SHM is doubled while its mass and angular frequency stay the same, by what factor does its total energy increase?

A particle executes SHM with amplitude A. At a displacement of A/3 from the mean position, what fraction of the total energy is kinetic?

For a particle executing SHM with amplitude A, at what displacement (as a fraction of A) is the kinetic energy exactly three times the potential energy?

Liquid oscillates in a U-tube with total column length 0.25 m. Taking g ≈ π² m/s², what is the time period of oscillation?

A damped oscillator's amplitude reduces to half its initial value every 20 oscillations. What fraction of the initial amplitude remains after 60 oscillations?

A damped oscillator is driven by an external periodic force. Under which condition is the amplitude of the resulting forced oscillation the largest?

Two simple pendulums of lengths 1.00 m and 0.81 m start swinging together in phase. After how many oscillations of the longer pendulum will they next be in phase together?

A ball is released (from rest) inside a frictionless tunnel drilled straight through the centre of the Earth. Taking Earth's radius as 6.4 × 10⁶ m and g = 9.8 m/s², find the time period of its oscillation.