Oscillations Physics - Oscillations

At which position the restoring force acting on a particle executing linear SHM is maximum?

Write the differential equation for angular S. H. M.

At which position, the total energy of a particle executing linear S. H. M. is purely potential?

What is perfectly black body?

The periodic time of a linear harmonic oscillator is \(2 \pi\) second, with maximum displacement of \(1 cm\). If the particle starts from extreme position, find the displacement of the particle after \(\frac{\pi}{3}\) seconds.

The maximum velocity of a particle performing linear S.H.M. is \(0.16 m / s\). If its maximum acceleration is \(0.64 m / s ^2\), calculate its period.

A body of mass \(1 kg\) is made to oscillate on a spring of force constant \(16 N / m\). Calculate: (a) angular frequency, (b) frequency of vibration.

A particle performing linear S. H. M. has maximum velocity \(25 cm / s\) and maximum acceleration \(100 cm / s ^2\), Find period of oscillation.

Define second's pendulum. Derive a formula for the length of second's pendulum

Derive an expression for period of a simple pendulum.

A simple pendulum of length \(1 m\) has mass \(10 g\), and oscillates freely with amplitude of \(5 cm\). Calculate its potential energy at extreme position.

Define linear S. H. M. Obtain differential equation of linear S. H. M.

From differential equation of linear S.H.M., obtain an expression for acceleration, velocity and displacement of a particle performing S.H.Μ.

Represent graphically the displacement, velocity and acceleration against time for a particle performing linear S.H.M., when it starts from the mean position.

Discuss the composition of two S.H.M.s along the same path having same period. Find the resultant amplitude and initial phase.

Define phase of S.H.M. Show variation of displacement, velocity and acceleration with phase for a particle performing linear S.H.M. graphically, when it starts from extreme position.

Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?

State the differential equation of linear simple harmonic motion. Hence obtain the expression for acceleration, velocity and displacement of a particle performing linear S.H.M.

Prove the law of conservation of energy for a particle performing simple harmonic motion. Hence graphically show the variation of kinetic energy and potential energy w. r. t. instantaneous displacement.