Question

A spring-mass system oscillates in a car. If the car accelerates on a horizontal road, the frequency of oscillation will:
(A) Increase
(B) Decrease
(C) Remain same
(D) Become zero

Answer 1

Hint: The frequency of the oscillation of a spring mass system is dependent on the value of the mass and the spring constant (force constant) of the spring. The spring constant and mass are independent of the acceleration the system may experience.

Formula used: In this solution we will be using the following formula;
 $ f = \sqrt {\dfrac{k}{m}} $ where $ f $ is the frequency of a spring mass system, $ k $ is the force constant of the spring, and $ m $ is the mass of the object hung on the spring.

Complete step by step solution:
In general, a spring mass system is a system where an object with mass is hung on a spring, which is then displaced. After displacement, the spring mass system has an oscillatory motion. As in all oscillatory motion, it oscillates with a particular frequency. The frequency for a spring mass system is given by
 $ f = \sqrt {\dfrac{k}{m}} $ where $ k $ is the force constant of the spring, and $ m $ is the mass of the object hung on the spring.
Now, since neither of these quantities is dependent on the acceleration of the system, if the acceleration is increased, neither the spring constant nor the mass will change. Hence the frequency remains constant.
Hence, the correct option is C.

Note:
For clarity, this doesn’t imply that the acceleration has no effect on a spring mass system, it just means it has no effect on the frequency of the system. The acceleration has an effect on the equilibrium position of the system. For example, if the system was not oscillating and is in equilibrium, the position of the mass will shift in the direction opposite that of the acceleration.