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 the mass but the amplitude of its oscillations remains the same,then the maximum speed of the block will a. increase by a factor of 2 b. decrease by a factor of 2^1/2 c. decrease by a factor of 4 d. decrease by a factor of 2

The correct answer is d. decrease by a factor of 2.<br /><br />When a block undergoes simple harmonic oscillations on the end of an ideal spring, the maximum speed of the block is given by the formula:<br /><br />v_max = Aω<br /><br />where A is the amplitude of the oscillations and ω is the angular frequency.<br /><br />The angular frequency ω is related to the mass m and the spring constant k by the formula:<br /><br />ω = √(k/m)<br /><br />Therefore, if the mass of the block is doubled, the angular frequency will decrease by a factor of √2. Since the amplitude remains the same, the maximum speed of the block will decrease by a factor of 2.