Spring constant, k=1200Ncalm−1
Mass, m=3kg
Displacement, A=2.0cm=0.02m
(i) Frequency of oscillation
v, is given by the relation:
v=1T=12π√km
where, T is time period
∴v=12×3.14√12003=3.18Hz
Hence, the frequency of oscillations is 3.18 cycles per second.
(ii) Maximum acceleration (a) is given by the relation:
a=ω2A
where,
ω= Angular frequency =√km
A = maximum displacement
∴a=kmA=1200×0.023=8ms−2
Hence, the maximum acceleration of the mass is 8.0m/s2
(iii) Maximum velocity, vmax=Aω
=A√km=0.02×√12003=0.4m/s
Hence, the maximum velocity of the mass is 0.4 m/s.