Question

A 140-g object is fixed to the end of a spring that has a spring constant of 15.0 N/m. The object is displaced 15.0 cm to the right and released from rest at t = 0 to slide on a horizontal, frictionless table

1)Calculate the first time when the object is at the equilibrium position

2)What is the first time when the object is 10.0 cm to the left of equilibrium?

3)What is the first time that the object is 5.00 cm to the right of equilibrium, moving toward the left?

please show your work and formulas used

Answer 1

m = 0.14 kg
k = 15 N/m
A = 0.15 m
1) T = 1/f
w = 2*pi*f = 2*pi/T
T = 2*pi/w = 2*pi*sqrppt(m/k) = 0.6070 s
time taken to reach equilibrium for the first time = T/4 = 0.15175 s
2) when x = -0.1m
but generally, x = Acos(wt) = 0.15*cos(10.35t) = -0.1
0.22 s
3) x = 0.05
0.15*cos(10.35t) = 0.05
t = 0.1189 s