The maximum restoring force of a body executi | vedclass

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Question

(A) The maximum restoring force $F$ for a body executing $SHM$ is given by $F = kA$,where $k$ is the force constant and $A$ is the amplitude.Given,$\a

Vedclass · Accepted Answer

$A = \frac{2\beta}{\alpha}$

Vedclass · Answer

(A) The maximum restoring force $F$ for a body executing $SHM$ is given by $F = kA$,where $k$ is the force constant and $A$ is the amplitude.Given,$\alpha = kA$  --- $(1)$The total energy $E$ of a body executing $SHM$ is given by $E = \frac{1}{2}kA^2$.Given,$\beta = \frac{1}{2}kA^2$ --- $(2)$Dividing equation $(2)$ by equation $(1)$:$\frac{\beta}{\alpha} = \frac{\frac{1}{2}kA^2}{kA}$$\frac{\beta}{\alpha} = \frac{A}{2}$Therefore,the amplitude $A$ is:$A = \frac{2\beta}{\alpha}$

The maximum restoring force of a body executing $SHM$ is $\alpha$ and the total energy is $\beta$. Obtain its amplitude in terms of $\beta$ and $\alpha$.

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