Answer the following SHM problems: An object is undergoing SHM with period 0.400
ID: 1624458 • Letter: A
Question
Answer the following SHM problems:
An object is undergoing SHM with period 0.400s and amplitude 6.00 cm. At t=0 the object is instantaneously at rest at x= 6.00 cm. Calculate the time it takes the object to go from x = 6.00 cm to x = -1.50 cm
B) A 50.0 g hard-boiled egg moves o the end of a spring with force constant k= 25.0 N/m. Its initial displacement is 0.300 m. A damping force Fx= bvx acts on the eggs, and the amplitude of the motion decreases to 0.100 m in 5.00 s. Calculate the magnitude of the damping constant b.
C)A hanging wire is 1.80 m long. When a 60.0 kg steel ball is suspended from the wire, the wire stretches by 2.00 mm. If the ball is pulled down a small additional distance and released, at what frequency will it vibrate? Assume that the stress on the wire is less than the proportional limit.
Explanation / Answer
(A) x = A cos(wt)
w = 2pi/T = 5pi
A = 6 cm
x = 6cm cos(5pi t)
- 1.50 = 6 cos(5pit)
5 pi t = 0.58pi
t = 0.116 sec
(B) a = a0 e^(-Bt)
0.10 = 0.3 e^( - 5B)
B = 0.22
B = b / 2 m
b = 0.22 x 2 x 0.050 = 0.022 N s / m
(c) F= kx - m g = 0
k (2 x 10^-3) = 60 x 9.8
k = 2.94 x 10^5 N/m
w = sqrt(k/m) = 70 rad/s
f = w / 2pi = 11.14 Hz