Question

A smooth inclined plane having angle of inclination 30 with the horizontal has a 2.5 kg mass held by a spring wch is fixed at the upper end. if the mass is taken 2.5 cm up along the surface of inclined plane, the tension in the spring reduces to zero. if the mass is now released the angular frequency of oscillation is

Answer 1

Hey dear,

● Answer - 14 rad/s

● Explaination-
When, tension in the spring reduces to zero.
Inclined force = Restoring force

At inclination = θ ,
mgsinθ = kx
2.5 × 9.8 × sin30 = k × 2.5×10^-2
9.8 × 1/2 = k / 100
k = 490 N/m

Angular frequency is given by,
w = √(k/m)
w = √(490/2.5)
w = √196
w = 14 rad/s

Angular frequency is 14 rad/Hz.

Hope this is hekpful...

Answer 2

Hey dear,

● Answer - 14 rad/s   OR ALSO  = g/root3

● Explaination-

When, tension in the spring reduces to zero.

Inclined force = Restoring force

At inclination = θ ,

mgsinθ = kx

2.5 × 9.8 × sin30 = k × 2.5×10^-2

9.8 × 1/2 = k / 100

k = 490 N/m

Angular frequency is given by,

w = √(k/m)

w = √(490/2.5)

w = √196

w = 14 rad/s

Angular frequency is 14 rad/Hz.

Hope this is hekpful...

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