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An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical spring of spring constant kH = 85 N/m, see Fig.1. The effect of the fluid resistance is governed by the damping constant b = 0.07kg/s. (i) Find the period of the damped oscillation. (ii) By what percentage does the amplitude of the oscillation decrease in each cycle?

An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical spring of spring
constant kH = 85 N/m, see Fig.1. The effect of the fluid resistance is governed by the
damping constant b = 0.07kg/s.
(i) Find the period of the damped oscillation.
(ii) By what percentage does the amplitude of the oscillation decrease in each cycle? 

Grade:12

1 Answers

Aryan
14 Points
one year ago
Time period T =2π 
k
m
​ 
 
​ 
 =0.1×π
Angular velocity ω= 
T
2π
​ 
 =20rad/s
for 'k' the spring constant at maximum reading x=0.25 m extension: 
M=10kg
Mg=−kx 
k- spring constant ; g -acceleration due to gravity 
k=392.4N/m
 
Now 
2π 
k
m
​ 
 
​ 
 =0.1×π
putting the value of k . 
m=0.98kg

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