Question

 particle is having kinetic energy 1/3 of the maximum value at a distance of 4 cm from the mean position, Find the amplitude of motion.

4 points

2√(6 cm)

2/√(6 cm)

√(2 cm)

6√(2 cm)

​

Answer 1

▶ Solution :

Given :

▪ A particle is performing SHM

▪ It has one-third of maximum kinetic energy at a distance of 4cm from the mean position.

To Find :

Amplitude of the particle

Formula :

Formula of kinetic energy of particle in SHM is given by

$\boxed{\bf{\pink{KE=\dfrac{1}{2}k(A^2-X^2)}}}$

• A denotes amplitude
• X denotes displacement from mean position
• k = mω$^2$

Calculation :

→ Maximum kinetic energy of particle in SHM is given by

$\star\:\bf\red{(KE)_{max}=\dfrac{1}{2}kA^2}$

ATQ,

$\mapsto\bf\:KE=\dfrac{(KE)_{max}}{3}\\ \\ \mapsto\sf\:\dfrac{1}{2}k(A^2-4^2)=\dfrac{\frac{1}{2}kA^2}{3}\\ \\ \mapsto\sf\:A^2=3(A^2-16)\\ \\ \mapsto\sf\:2A^2=48\\ \\ \mapsto\sf\:A^2=24\\ \\ \mapsto\boxed{\bf{\orange{A=2\sqrt{6}\:cm}}}$

Answer 2

2√(6 cm) is your Answer

hope it helps u...

follow me