Question

(a) Show that the centre of oscillation and centre
of suspension are interchangeable.​

Answer 1

Answer:

The time period about point of oscillation is same as the axis of suspension through S. Thus the centre of oscillation and oscillation are interchangeable. Figure shows a section of a rigid body of mass 'm' by a vertical plane passing though its centre of gravity 'G' and point of suspension 'S'.

Answer 2

Concept Introduction:-

Oscillation is the repeating or periodic change of a quantity around a middle value or among two or more states, often in time.

Explanation:-

A question has been provided to us

We need to find the solution to the question

If the pendulum be inverted and suspended about the axis of oscillation through $O$. Its time period will be obviously given by $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{k}^{2}+l^{\prime 2}}{\mathrm{~g} l^{\prime}}}$. And, since $\mathrm{k}^{2} / l=l^{\prime}$ we have $\mathrm{k}^{2}=l l^{\prime}$ so that the expression for the time period $t$ becomes $\mathrm{T}=2 \pi \sqrt{\frac{l l^{\prime} / l+l}{\mathrm{~g}}} \quad$ OR $\mathrm{T}=2 \pi \sqrt{\frac{l^{\prime}+l}{\mathrm{~g}}}$. The time period about point of oscillation is same as the axis of suspension through $\mathrm{S}$. Thus the centre of oscillation and oscillation are interchangeable.

Centre of percussion

Final Answer:-

The correct answer is Centre of percussion.

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