Question

A spring with a spring constant 1200 Nm-1

is mounted on a horizontal table and one end is fixed. 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 cm

and released. Calculate (a) the frequency of oscillation of the mass, (b) the maximum acceleration of the

mass and (c) the maximum speed of the mass.​

Answer 1

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.

Explanation:

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