Simple harmonic motion oscillate. What is the total energy

[firezap]

Homework Statement

The position of a 50 g oscillating mass is given by x(t)=(2.0cm)cos(10t−π/4), where t is in s. If necessary, round your answers to three significant figures. Determine: The total energy.

Homework Equations

T = 2π/w
T = 2π√m/k
1/2kA^2
1/2mv^2
1/2kx^2

The Attempt at a Solution

T = 2π/10 = 0.6283s
k = 0.5kg / (0.6823/2π)^2 = 5.000N/m
1/2kA^2 = 0.5(5)(0.02)^2 = 0.001J

 

[Nathanael]

Your answer is right.

In my opinion, it's more straightforward to find the answer from the maximum kinetic energy. Find the amplitude of dx/dt, which is the maximum velocity, which can be used to find the maximum kinetic energy (which equals the total energy because at that moment there's no potential energy).

But whichever way you like best is good.