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erastova [34]
2 years ago
12

A mass of 148g stretches a spring 6cm. The mass is set in motion from its equlibrium position with a downward velocity of 10cm/s

and no damping is applied. Determine the position u of the mass at any time t. Use 9.8m/s2 as the acceleration due to gravity. Pay close attention to the units.
Physics
1 answer:
zalisa [80]2 years ago
7 0

Answer:

u(t)=0.78sin12.78t

Explanation:

We are given that

Mass,m=148 g

Length,L=6 cm

Velocity,u'(0)=10 cm/s

We have to find the position u of the mass at any time t

We know that

\omega_0=\sqrt{\frac{g}{L}}=\sqrt{\frac{980}{6}}=12.78 rad/s

Where g=980 cm/s^2

u(t)=Acos12.78 t+Bsin 12.78t

u(0)=0

Substitute the value

A=0

u'(t)=-12.78Asin12.78t+12.78 Bcos12.78 t

Substitute u'(0)=10

12.78B=10

B=\frac{10}{12.78}=0.78

Substitute the values

u(t)=0.78sin12.78t

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