EASY
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A particle executingS.H.M. its potentialenergy V/S displacement graph is given by
The value of restoring force constant is :

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Important Questions on Simple Harmonic Motion

MEDIUM
A particle is executing simple harmonic motion (SHM) of amplitude A, along the x -axis, about x=0. When its potential Energy PE equals kinetic energy KE, the position of the particle will be:
EASY

Total energy of a particle performing S.H.M. is NOT proportional to

EASY

An object of mass 4 kg is attached to a spring which is fixed at one end on a rigid support and the mass-spring system is kept on a frictionless table. The object is allowed to execute simple harmonic motion along X - direction. The force constant of the spring is 10 N m-1 and the spring is stretched initially a distance of 5 cm, the total energy stored in the system is

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MEDIUM
A particle starts executing simple harmonic motion (SHM) of amplitude a and total energy E. At any instant, its kinetic energy is 3E4, then its displacement y is given by:
EASY

A body of mass 1 kg is executing simple harmonic motion. Its displacement ycm at t seconds is given by y=6sin100t+π4. Its maximum kinetic energy is

HARD
In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.
EASY
For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?
MEDIUM

A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed ?

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EASY
The physical quantity conserved in simple harmonic motion is
MEDIUM
The total energy of a body executing simple harmonic motion is E. The kinetic energy when the displacement is 1/3 of the amplitude
EASY
Total energy of a particle of mass ' m ' executing SHM given by y = Asinωt for any displacement is:
EASY
A simple pendulum of length L has mass M and it oscillates freely with amplitude A. At the extreme position, its potential energy is (g = acceleration due to gravity)
MEDIUM
A body is executing simple harmonic motion with frequency n, the frequency of its potential energy is
HARD
An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant t=T4 s starting from mean position. Assume that the initial phase of the oscillation is zero.
MEDIUM
For a body executing S.H.M. :
(a) Potential energy is always equal to its K.E.
(b) Average potential and kinetic energy over any given time interval are always equal.
(c) Sum of the kinetic and potential energy at any point of time is constant.
(d) Average K.E. in one time period is equal to average potential energy in one time period.
Choose the most appropriate option from the options given below :
MEDIUM
A particle of mass 1 kg is hanging from a spring of force constant 100 N m-1. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The minimum time when the kinetic energy and potential energy of the system will become equal, is Tn. The value of n is ________.
EASY

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.

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The potential energy U(x) versus time t plot of the particle is correctly shown in figure:

EASY
A body is executing S.H.M. Its potential energy is E1 and E2 at displacements x and y respectively. The potential energy at displacement x+y is
MEDIUM
The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is
MEDIUM
A particle is executing simple harmonic motion with a time period T. At time t=0, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like: