A mass is bouncing on the end of a spring with a period T when measured by a ground observer.What would the period of oscillation be (as measured by the same observer)if the mass and spring were moving past the ground observer at a speed of 0.80 c?
A)0.44 T
B)0.60 T
C)1.0 T
D)1.7 T

Question

Quizplus · Accepted Answer

This problem is related to time dilation, a consequence of Einstein's theory of special relativity. The period of the bouncing motion (T) is a proper time interval, which is the time interval measured in the reference frame of the spring and mass. When this system is moving with a relativistic speed v = 0.80c relative to the ground observer, the period will appear longer to the ground observer because of time dilation. The time dilation factor γ can be calculated as follows:

γ = 1/√(1-(v/c)^2) = 1/√(1-0.8^2) = 1/0.6 = 1.67

The period measured by the ground observer (T') can be found by multiplying the proper period by the time dilation factor:

T' = γT = 1.67T

Therefore, the answer is D) 1.7 T.

A Mass Is Bouncing on the End of a Spring