Question

A block with mass m = 0.1 kg undergoes periodic motion with frequency f = 0.1 Hz, with amplitude A = 0.5 m. It starts at position x = -0.5 m. Determine the equation of oscillation, explicitly stating the angular frequency , maximum velocity vmax, and total energy of the oscillator. Also sketch a plot of position, velocity, and energy as functions of time, and explain qualitatively how these are related.

Answer 1

The angular frequency is

The equation of oscillation is

At t=0, x=-0.5 m = -A

Therefore the phase is 180 degrees o Pi radians

Therefore the equation is

the unit is meters in the above equation

The maximum velocity is

The total energy is

In the above figures, the position(x) plot with time is a negative cos curve as is obvious from the position equation above

The velocity is the time derivative of position and hence is a sine curve

The total energy is constant and hence is a straight line.