Question

A mass m is suspended from a spring of spring constant k and oscillates with a certain period t. If you are going to replace the spring with a new spring with a different spring constant, what should the new constant be to get a period of 2t?

A) k
B) 2k
C) 4k
D) 8k

Answer 1

To achieve a period of 2T for a spring oscillator, the new spring constant must be one-fourth of the original spring constant, which means none of the given options A) k, B) 2k, C) 4k, or D) 8k are correct; the correct option should be 1/4k.

Step-by-step explanation:

The period T of a mass m oscillating on a spring with spring constant k is given by the formula T = 2π √(m/k). If we wish to double the period to 2T, we can set up the equation 2T = 2π √(m/k'), where k' is the new spring constant.

Squaring both sides of the equation to remove the square root and then solving for k' yields that k' must be one-fourth the original constant k in order to achieve the new period of 2T.

Therefore, the correct answer is C) 1/4k, which is none of the options provided. The given options might be based on an incorrect interpretation of the question, possibly due to a typo or misunderstanding.