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Oscillations

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Question : 9
Total: 25
A spring having a spring constant 1200 N m‌–1 is mounted on a horizontal table as shown in figure. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.
Determine (i) the frequency of oscillations of the mass, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.
Solution:  
Here, m = 3.0 kg ; k = 1200 N m‌–1, A = 2 cm = 0.02 m
(i) The frequency of oscillations of the attached mass is
υ=
1
2π
√
k
m
 =
1
2×3.14
√
1200
3
=3.2s−1
(ii) The maximum acceleration of the mass is
|amax|=ω2A=
kA
m
(∵ω=√
k
m
)
=
1200×0.02
3
=8ms−2
(iii) The maximum speed of the mass is
vmax=Aω=A√
k
m
 =0.02×√
1200
3
=0.4ms−1
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