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Example Calculation Simple Harmonic Vibration # Calculation Example – Simple harmonic vibration part 2

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A single point with mass m is vibrating harmonically. The displacement x from point of balance is governed by the differential equation

where ω is a positive constant.

b) What is the speed, the acceleration, and the force at the mass as a function of time t and constants A, B.

**Solution**

The derivative of x(t)=A sinωt+B cos ωt

is the speed u(t)=x'(t)=Aω cosωt-B ωsinωt

And the derivative of speed is the acceleration

a(t)=u'(t)=x''(t)=-〖ω^2 Α sin〗ωt-ω^2 B cosωt

The force at the mass is

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