Question

A 1.20 kg mass on a horizontal spring oscillates on a frictionless surface with a displacement as a function of time given by x(t) = 0.075cos(4.16t – 2.45). (Units are standard units.)
a.) Find the time for one complete vibration.
b.) Find the force constant of the spring.
c.) Find the maximum force on the mass.
d.) Find the maximum speed of the mass.
e.) Find the position, speed and acceleration of the mass at t = 1.00 s.
f.) Find the total energy of the oscillating spring.

Answer 1

a. when is 4.16 t = 2 pi ? Then t = T =2 pi/4.16

b. 2 pi f = sqrt (k/m)
so
2 pi/T = 4.16 = sqrt (k/1.2)

c. F = -k x
we know k now and max x = .075

d. dx/dt max = (4.16)(.075)

e. we have everything but acceleration
v = -.075(4.16)(sin( ) )
a = - (4.16)^2 x

f. we have v max
(1/2) m v^2 is total when v = v max