Home
Class 11
PHYSICS
If a body is executing simple harmonic m...

If a body is executing simple harmonic motion and its current displacement is `sqrt(3)//2` times the amplitude from its mean position , then the ratio between potential energy and kinetic energy is

A

`3:2`

B

`2:3`

C

`sqrt(3):1`

D

`3:1`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) The current displacement is `(sqrt(3))/(2)` times the amplitude
i.e., `y=(sqrt(3))/(2)A`
we know that potential energy of a body in SHM is given by where, m and `omega` are constant.
`U=(1)/(2)momega^(2)y^(2)`
`U=(1)/(2)momega^(2)((sqrt(3))/(2)A)^(2)=(1)/(2)momega^(2)xx(3A^(2))/(4)" "...(i)`
Similarly
Kinetic energy of a body in SHM is given by
`K=(1)/(2)momega^(2)(A^(2)-y^(2))=(1)/(2)momega^(2)(A^(2)-(3A^(2))/(4))=(1)/(2)momega^(2)(A^(2))/(4)" "...(ii)`
So, the ratio of PE and KE
`PE: KE =(1)/(2)momega^(2)xx(3A^(2))/(4):(1)/(2)momega^(2)(A^(2))/(4)=3:1`
Promotional Banner

Similar Questions

Explore conceptually related problems

A body is vibrating in simple harmonic motion . If its acceleration in 12 cms^(-2) at a displacement 3 cm from the mean position, then time period is

A body is executing simple harmonic motion. At a displacement x (from its mean position) its potential energy is E_(1) and at a displacement y its potential energy is E_(2) . The potential energy is E at displacement (x+y) . Then:

A body is executing simple harmonic motion with frequency 'n' the frequency of its potential energy is

A body is executing simple harmonic motion. At a displacement x, its potential energy is E_1 and a displacement y, its potential energy is E_2 . The potential energy E at a displacement (x+y) is

A body is executing simple harmonic motion As x displacement x its potential energy is E_(1) and at a displacement y its potential energy is E_(2) The potential energy E at displacement (x+y) is

The total meachanical energy of a particle executing simple harmonic motion is E when the displacement is half the amplitude is kinetic energy will be

The total energy of a particle, executing simple harmonic motion is. where x is the displacement from the mean position, hence total energy is independent of x.

A body is executing simple harmonic motion. At a displacement x from mean position, its potential energy is E_(1)=2J and at a displacement y from mean position, its potential energy is E_(2)=8J . The potential energy E at a displacement (x+y) from mean position is

A particle executes simple harmonic motion with an amplitude 9 cm. At what displacement from the mean position, energy is half kinetic and half potential ?