A particle of mass m is executing SHM about the origin on x -axis with frequency √(k a/π m), where k is a constant and a is the amplitude. Find its potential energy, if x is the displacement at time t :

Question

A particle of mass m is executing SHM about the origin on x -axis with frequency √(k a/π m), where k is a constant and a is the amplitude. Find its potential energy, if x is the displacement at time t : (A) k a x2 (B) k a2 x (C) 2 π k a x2 (D) 2 π k x3

Tardigrade Admin · Accepted Answer

2 π f=ω ; 2 π √(k a/π m)=ω Potential energy U=(1/2) m ω2 x2=2 π kax 2

Q. A particle of mass $m$ is executing SHM about the origin on $x$ -axis with frequency $\frac{ka}{πm}$ , where $k$ is a constant and $a$ is the amplitude. Find its potential energy, if $x$ is the displacement at time $t$ :

$ka x^{2}$

$k a^{2} x$

$2 πka x^{2}$

$2 πk x^{3}$

$2 π f = ω; 2 π \frac{ka}{πm} = ω$
Potential energy $U = \frac{1}{2} m ω^{2} x^{2} = 2 πka x^{2}$

Q. A particle of mass m is executing SHM about the origin on x -axis with frequency πmka​​, where k is a constant and a is the amplitude. Find its potential energy, if x is the displacement at time t :

kax2

ka2x

2πkax2

2πkx3