As shown in the figure (a) below, a mass m =50.0 g is attached to an ideal massl
ID: 1562717 • Letter: A
Question
As shown in the figure (a) below, a mass m =50.0 g is attached to an ideal massless spring with spring constant k. The mass is set into oscillating motion, and the period of oscillation is measured to be T = 1.00 10^-1 s. (a). What is the spring constant k? (assume no friction in the system) Now as shown in figure (b) below, a damper is added to the system. The mass is set into oscillating motion, and the period of oscillation is now measured to be T = 8.20 10^-2 s. (b) What is the damping constant b ? (c)How many oscillations does the damped system make before the amplitude of the oscillation has decreased to 20% of the initial amplitude?Explanation / Answer
a)
Tme period of SHM = 2[m/k]^1/2
T = 0.1 sec; m = 0.05 kg
T2 = 42m/k
k = 42m / T2
= 197.39
b)
' = [k/m - b2/4m2]
here k/m = 197.39/ 0.05 = 3947.8
' = [3947.8 - 100 b2 ]
frequency = [3947.8 - 100 b2 ] / 2
12.195 x 2 = 3947.8 - 100 b2
b = 6.221
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