Physics - SHM Question with Solution | TestHub

Given displacement $Y=A\cos 30^{\circ }=A\frac{\sqrt{3}}{2}$

Kinetic energy of a particle in S.H.M. is given by:

$K=\frac{1}{2}k(A^2-Y^2)$

Substituting the value of $Y$:

$K=\frac{1}{2}k\left(A^2-\frac{3A^2}{4}\right)=\frac{1}{8}k{A}^2$

Given $K=200\text{ J}$ and $A=40\text{ cm}=0.4\text{ m}$:

$200=\frac{1}{8}k(0.4{)}^2$

$200=\frac{1}{8}k(0.16)$

$200=0.02k$

$k=\frac{200}{0.02}=10000\text{ N/m}=1\times 10^4\text{ N/m}$

Comparing with $k=1\times 10^x\text{ N/m}$, we get $x=4$.

Answer: 4