Question

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 30 cm/s, and if there is no damping, determine the position u of the mass at any time t. (Use g = 9.8 m/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds.)

Answer 1

`u(t)=(15)/(7)*sin(14t)`

Step-by-step explanation:

Given

`m=100g`

`L=5cm`

`u(0)=0`

`u(0)'=30(cm)/(s)`

The function that describe the motion is:

`u(t)=A*cos(wt)+b*sin(wt)`

`w_(o)^2=(g)/(L)`

`w_(o)^2=(9.8(m)/(s^2))/(0.05m)`

`w=\sqrt{196(m^2)/(s^2)}=14(m)/(s)`

`u(t)=A*cos(14t)+B*sin(14t)`

`u(0)=0+30=B*sin(14)`

`14B=30`

`B=(15)/(7)`

`u(t)=(15)/(7)*sin(14t)`