The kinetic energy of a particle,executing si | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given: Kinetic Energy $(K.E.)$ at mean position $= 16 \ J$,Amplitude $(A)$ $= 25 \ cm = 0.25 \ m$,Mass $(m)$ $= 5.12 \ kg$.The kinetic energy at t

Vedclass · Accepted Answer

$\frac{\pi}{5} \ s$

Vedclass · Answer

(A) Given: Kinetic Energy $(K.E.)$ at mean position $= 16 \ J$,Amplitude $(A)$ $= 25 \ cm = 0.25 \ m$,Mass $(m)$ $= 5.12 \ kg$.The kinetic energy at the mean position is equal to the total energy $(E)$ of the particle in simple harmonic motion.The formula for total energy is $E = \frac{1}{2} m \omega^2 A^2$.Substituting the values: $16 = \frac{1}{2} 	imes 5.12 	imes \omega^2 	imes (0.25)^2$.Solving for $\omega^2$: $\omega^2 = \frac{16 	imes 2}{5.12 	imes 0.0625} = \frac{32}{0.32} = 100$.Therefore,$\omega = \sqrt{100} = 10 \ rad/s$.The period of oscillation $(T)$ is given by $T = \frac{2 \pi}{\omega}$.Substituting $\omega$: $T = \frac{2 \pi}{10} = \frac{\pi}{5} \ s$.

The kinetic energy of a particle,executing simple harmonic motion is $16 \ J$ when it is in the mean position. If the amplitude of motion is $25 \ cm$ and the mass of the particle is $5.12 \ kg$,the period of oscillation is

Similar Questions

The average kinetic energy in one time period of a $SHM$ is :-

What is the displacement of a body in $SHM$ when the potential energy becomes three times its kinetic energy?

The graphs in the figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graph best represents the relationship obtained when $y$ is the total energy of the system?

The potential energy of a particle with displacement $X$ is $U(X)$. The motion is simple harmonic,when ($K$ is a positive constant)

If the amplitude of linear $S.H.M.$ is decreased,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module