Question

A block is attached to an ideal spring undergoes simple harmonic oscillations of amplitude A. Maximum speed of block is calculated at the end of the spring. If the block is replaced by one with twice the mass but the amplitude of its oscillations remains the same, then the maximum speed of the block will

• A. decrease by a factor of 4
• B. decrease by a factor of 2
• C. decrease by a factor of $\sqrt{2}$
• D. remain the same
• E. increase by a factor of 2

Answer 1

Answer: (C)

decrease by a factor of $\sqrt{2}$

Maximum speed of the block $V_{max}=wA$ where $w=\sqrt{\frac{k}{m}}$

$⟹$ $V_{max}=\sqrt{\frac{k}{m}}A$ where $k=constant$

Now the mass is doubled i.e $m^{\prime }=2m$ keeping $A=constant$

$\therefore$ $V_{max}^{\prime }=\sqrt{\frac{k}{2m}}A=\frac{V_{max}}{\sqrt{2}}$

Thus speed is decreased by a factor of $\sqrt{2}$.