A simple harmonic oscillator consists of a mass m and an ideal spring with spring constant k. The particle oscillates as shown in (i) with period T. If the spring is cut in half and used with the same particle, as shown in (ii), the period will be:
A) 2T
D) T
E) T/2

Question

A simple harmonic oscillator consists of a mass m and an ideal spring with spring constant k. The particle oscillates as shown in (i) with period T. If the spring is cut in half and used with the same particle, as shown in (ii), the period will be: 
A) 2T 
D) T 
E) T/2

Quizplus · Accepted Answer

The period of a simple harmonic oscillator is given by:
T = 2π√(m/k)
When the spring is cut in half, the spring constant becomes 2k, since two springs in parallel have a combined spring constant of k/2 + k/2 = k. Therefore, the new period is:
T' = 2π√(m/2k)
Dividing T' by T, we get:
T'/T = √(k/2k) = 1/√2
Therefore, the new period is T/√2, which is approximately 0.71T. The answer choice closest to this value is C, 11eaafb8_0021_ce59_a7a5_b78086c1a473_TB3150_11, which is approximately 0.75T, so C is the best choice.

A Simple Harmonic Oscillator Consists of a Mass M and an Ideal