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Example Calculation Simple Harmonic Vibration
Calculation Example – Simple harmonic vibration part 2
This calculation is an example problem in structural engineering. This content is sponsored by PPI. For similar problems, see the list of review books by PPI
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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