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Tuesday, 12 June 2018 11:45cat

Calculation Example – Simple harmonic vibration part 2 Featured

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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.



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

is the speed       u(t)=x'(t)=Aω cos⁡ωt-B ωsin⁡ωt 


And the derivative of speed is the acceleration

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

The force at the mass is


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