A10 kg mass stretches a spring 70 cm in equilibrium. suppose a 2 kg mass is attached to the spring, initially displaced 25 cm below equilibrium, and given an upward velocity of 2 m/s. find its displacement for t > 0. find the frequency, period, amplitude, and phase angle of the motion

Explanation:

1. Find spring constant k. From a free body diagram, you will get the forces on  the 10 kg mass, with a displacement d. It will be gravity pulling the mass down and the spring force pulling the mass up. The 10 kg mass is in equilibrium. The resulting equation will be:

2. Use the result from 1. to find the equations of motion. In general they are given by:

, where ω is:

To find the amplitude A and the phase angle Ф, use the given initial conditions:

m₂ = 2 kg, x(0) = -0.25 m, v(0) = 2m/s

Solving for Ф:

Solving for A:

The equation for x(t) is now:

The frequency f is given by:

The period T is given by:

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14