Physics Question Help please!!!?

A 3.70 kg mass attached to a spring oscillates with a period of 0.375 s and an amplitude of 17.0 cm.

(a) Find the total mechanical energy of the system

w=sqrt(k/m)

so k= m w^2
at time=0

PE= 1/2 k x^2= 1/2 .17^2 w^2 m
and that is total energy when at t=0, velocity is zero.

To find the total mechanical energy of the system, you need to use the equation:

Total mechanical energy = kinetic energy + potential energy.

First, let's find the kinetic energy. The kinetic energy of an object is given by the equation:

Kinetic energy = (1/2) * mass * velocity^2.

Since the object is oscillating, we need to find the maximum velocity. The maximum velocity can be calculated by multiplying the amplitude of the oscillation by the angular frequency:

Maximum velocity = amplitude * angular frequency.

The angular frequency can be found using the equation:

Angular frequency = (2π) / period.

Now that we know the maximum velocity, we can calculate the kinetic energy.

Next, let's find the potential energy. The potential energy of an object attached to a spring is given by the equation:

Potential energy = (1/2) * spring constant * displacement^2.

To find the spring constant, we need to use the equation:

Angular frequency = √(spring constant / mass).

By rearranging the equation, we can solve for the spring constant.

Now, we can calculate the potential energy using the displacement of the oscillation.

Finally, we can add the kinetic energy and potential energy to find the total mechanical energy of the system.