Physics - SHM Question with Solution | TestHub

The restoring force is given by $F=-Kx$.

The potential energy of the body at displacement $x$ is $U=\frac{1}{2}K{x}^2$.

The kinetic energy of the body is $K.E.=\frac{1}{2}m{v}^2=\frac{1}{2}m{\omega }^2(a^2-x^2)$.

Since ${\omega }^2=\frac{K}{m}$, the kinetic energy can be written as $K.E.=\frac{1}{2}K(a^2-x^2)$.

The total energy of the body is $E=U+K.E.=\frac{1}{2}K{x}^2+\frac{1}{2}K(a^2-x^2)=\frac{1}{2}K{a}^2$.

Thus, the total energy depends only on the force constant $K$ and the amplitude $a$.

Answer: $K,a$