A student measures the maximum speed of a block undergoing simple harmonic oscillations of amplitude $A$ on the end of an ideal spring. If the block is replaced by one with twice its 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) increase by a factor of $2$
A) decrease by a factor of $4$
B) decrease by a factor of $2$
C) decrease by a factor of $\sqrt{2}$
D) increase by a factor of $2$
As we derived in Example 2, the maximum speed of the block is given by the equation $v_{max}=A\sqrt{\displaystyle \frac{k}{m}}$. Therefore, $v_{max}$ is inversely proportional to $\sqrt{m}$. If $m$ is increased by a factor of $2$, then $v_{max}$ will decrease by a factor of $\sqrt{2}$.