Question

A 50.6g mass connected to a spring with a force constant of 33.1N/m oscillates on a horizontal, frictionless surface with an amplitude of 3.90cm. Calculate the total energy of the system.

Calculate the speed of the mass when the displacement is 1.10cm.

Calculate the kinetic energy when the displacement is 2.80cm.

Calculate the potential energy when the displacement is 2.80cm.

Answer 1

As the kinetic energy at any displacement $x$ is $\frac{1}{2}k(A^2-x^2)$

So, $\frac{1}{2}mv^2=\frac{1}{2}k(A^2-x^2)$

Hence, $v=0.95697\frac{m}{sec}$

Kinetic energy at $x=2.80cm$

Kinetic energy$=\frac{1}{2}k(A^2-x^2)=0.01219J$

Potential energy at $x=2.80cm$

Potential energy$=\frac{1}{2}kx^2=0.01297J$