Question

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.

Answer 1

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

$u(t)=0.78sin12.78t$