Home
Class 11
PHYSICS
A particle of mass 0.50 kg executes a si...

A particle of mass 0.50 kg executes a simple harmonic motion under a force `F=-(50Nm^-1)x`. If it crosses the centre of oscillation with a speed of `10ms^-1`, find the amplitude of the motion.

Text Solution

Verified by Experts

The kinetic energy of the pasrticle when it is at the centre of oscillation si `E=1/2mv^2`
`=1/2(0.50kg)(10ms^-1)^2`
`=25J`
The potential energy is zero here. At the maximum displacement `x=A`, the speed is zero and hence the kinetic energy is zero. The potential energyi here is `1/2kA^`. As there is no loss of energy.
`=1/2kA^2=25J` .............i
The force on the particle is given by
`F=(50Nm^-1)mx`.
Thus the spring constant is `k=50Nm^-1` Equation i gives
`=1/2(50Nm^-1)A^2=25J`
o `A=1m`
Promotional Banner

Similar Questions

Explore conceptually related problems

A particle executes simple harmonic motion according to equation 4(d^(2)x)/(dt^(2))+320x=0 . Its time period of oscillation is :-

A particle of mass 4kg moves simple harmonically such that its PE (U) varies with position x, as shown. The period of oscillations is :-

A particle executes simple harmonic motion with a period of 16s . At time t=2s , the particle crosses the mean position while at t=4s , its velocity is 4ms^-1 amplitude of motion in metre is

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm"/"s . The frequency of its oscillation is……….

A particle executes simple harmonic motion with an amplitude A. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude form the equilibrium position is………..

When a body executes a simple harmonic motion and makes (1)/(2pi) oscillations, then its phase increases to………rad. (Fill in the blank).

A particle (bob) of mass 1 kg is performing vertical cicular motion. Then :

The maximum velocity of a particle executing simple harmonic motion with an amplitude 7 mm is 4.4 m/s. The period of oscillation is.

A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilinrium to the end is.

A particle executes simple harmonic motion with frequency f. The frequency of its potential and kinetic energy is………