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Simple Harmonic Oscillation

A rod of mass...

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A rod of mass M and length 2L is suspendedat its middle by a wire. It exhibits torsionaloscillations. If two masses each of m areattached at distance L/2 from its centre onboth sides, it reduces the oscillation frequencyby 20%. The value of ratio m/M is close to

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Q. A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are
attached at distance

^{'} L / 2^{'}

from its centre on both sides, it reduces the oscillation frequency by

20 %

. The value of ratio m/M is close to :

Q. A rod of mass

^{'} M^{'}

^{'} 2 L^{'}

is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance

^{'} L / 2^{'}

from its centre on both sides, it reduces the oscillation frequency by

20

%.
The value of ratio

m / M

Q. A rod of mass

M

2 L

is supended at its middle by a wire. It exhibits torsional oscillations. If two masses each of

m

are attached at distance

\frac{L}{2}

from its centre on both sides, it reduces the oscillation frequency by

20 %

. The value of ratio

\frac{m}{M}

Q. A thin rod of mass

0.3 k g

0.2 m

is suspended horizontally by a metal wire which passes through its centre of mass and is perpendicular to its length. The rod is set to torsional oscillation with a period of

2 s

. The thin rod is replaced by an equilateral triangular lamina which is suspended horizontally from its centre of mass. If its period of oscillations is found to be

10 s

, the moment of inertia of the triangular lamina about the axis of suspension is approximately.

m

\frac{m}{2}

are connected at the two ends of a massless rigid rod of length

l

. The rod is suspended by a thin wire of torsional constant

k

at the centre of mass of the rod-mass system (see figure). Because of the torsional constant

k

, the restoring torque is

τ = k θ

for angular displacement

θ

. If the rod is rotated by

θ_{0}

and released, the tension in it when it passes through its mean position will be:

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