A 192 g mass lying on a frictionless table is attached to a horizontal spring with a spring
constant of 372 N/m. The spring is stretched a distance of 29 cm (0.29 m).
(a) What is the initial potential energy of the system?
(b) What is the kinetic energy of the system when the mass returns to the equilibrium position
after being released?
Answers
A spring having with a spring constant 1200 N m
−1
is mounted on a horizontal table as shown in the 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, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.
ANSWER
Spring constant, k=1200m
−1
Mass, m=3kg
Displacement, A=2.0cm=0.02m
(i) Frequency of oscillation v, is given by the relation:
v=
T
1
=
2π
1
m
k
where, T is time period
∴v=
2×3.14
1
3
1200
=3.18Hz
Hence, the frequency of oscillations is 3.18 cycles per second.
(ii) Maximum acceleration (a) is given by the relation:
a=ω
2
A
where,
ω= Angular frequency =
m
k
A = maximum displacement
∴a=
m
k
A=
3
1200×0.02
=8ms
−2
Hence, the maximum acceleration of the mass is 8.0m/s
2
(iii) Maximum velocity, v
max
=Aω
=A
m
k
=0.02×
3
1200
=0.4m/s
Hence, the maximum velocity of the mass is 0.4 m/s.
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