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Snezhnost [94]
3 years ago
11

A mass of 100 g stretches a spring 5 cm. If the mass is set in motion from its equilibrium position with a downward velocity of

70 cm/s, and if there is no damping, determine the position u of the mass at any time t. (Use g
Physics
1 answer:
Rudiy273 years ago
3 0

Answer:

Explanation:

Given

mass of spring m=100\ gm

extension in spring x=5\ cm

downward velocity v=70\ cm/s

Position in undamped free vibration is given by

u(t)=A\cos \omega _0t+B\sin \omega _0t

where \omega _0^2=\frac{k}{m}

also \frac{k}{m}=\frac{g}{L}

\omega _0^2=\frac{k}{m}=\frac{9.8}{0.05}

\omega _0=14

u(t)=A\cos(14t)+B\sin(14t)

it is given

u(0)=0

u'(0)=70\ cm/s

substituting values we get

A=0

u(t)=B\sin (14t)

u'(t)=14B\cos (14t)

70=14B

B=\frac{10}{2}

B=5

u(t)=5\sin (14t)

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If you haven't learned about velocity yet, just think about it as speed for now. The funny-looking triangle, ∆, is a symbol for "the change of." For example, if I started walking at 3 \frac{feet}{second} then sped up to 5 \frac{feet}{second}, then the change in my speed would be 2 \frac{feet}{second}, because I started walking 2 \frac{feet}{second} faster!

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We have our answer! The car's acceleration is 3 meters per second^{2}.

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