Asked by Anonymous
Verify that the formula u(t)=Acos(ωo*t+Φ) is a solution to the differential equation for the mass on a spring, by plugging this expression for u(t) directly into the differential equation: d^2u/dt^2+ωo^2*u=0.
Answers
Answered by
bobpursley
Take the first derivative of U
u'=-Awosin(wo*t+...)
u"=-A wo^2 sin(wo*t+...)=-A wo^2 u
substitute into the org equation
-A wo^2 +wo^2(A)=o
O=O
u'=-Awosin(wo*t+...)
u"=-A wo^2 sin(wo*t+...)=-A wo^2 u
substitute into the org equation
-A wo^2 +wo^2(A)=o
O=O
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