Physics - SHM Question with Solution | TestHub

Total energy of the particle is the sum of kinetic and potential energy:

$E=K+U=2+1.2=3.2$ J

The angular frequency of the simple harmonic motion is:

$\omega =2\pi f=2\pi \left(\frac{16}{\pi }\right)=32$ rad/s

The total energy in SHM is given by:

$E=\frac{1}{2}m{\omega }^2{A}^2$

Substituting the given values:

$3.2=\frac{1}{2}\times 0.4\times (32{)}^2\times A^2$

$3.2=0.2\times 1024\times A^2$

$A^2=\frac{3.2}{204.8}=\frac{1}{64}$

$A=\frac{1}{8}=0.125$ m

Answer: $0.125$ m