Question

y''(t)= -y(t) + s(t) y(0) = y'(0) = 0 solution: y(t) = sin(t) Explain the physical...

y''(t)= -y(t) + s(t)

y(0) = y'(0) = 0

solution: y(t) = sin(t)

Explain the physical meaning of the DE above and its solution in terms of the mass-spring system.

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Answer #1

Doubt in this then comment below.. i will explain you..

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Please thumbs up for this solution...thanks.

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given is

y''+y= s(t) ....

Here , we see that damping coefficient is 0 ....it means there is no resistance in motion...

Also , y(0)=0 ... It means spring starts from equillibrium position..

y'(0)=0 ...it means that spring starts motion from rest ..

S(t) is the external force acts on the system

Its solution is sin(t) ..

This is periodic function whose amplitude is 1 , frequency is 1 and period is 2*pi ..

Spring moves up and down between fixed position ... No decreament in its amplitude takes place

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