Shown below are four spring-cart systsems that consist of a spring connected to

Question

Shown below are four spring-cart systsems that consist of a spring connected to a cart. All systems are shown with the cart located at the equilibrium position. The cart is resting on a horizontal frictionless surface. If the cart is pulled to the right a small distance and released, the mass will oscillate back and forth. The amplitude of oscillation, mass of the cart and spring constants for the four cases are provided in the figure. Rank the cases shown based on their frequency of oscillation from greatest to least.

Please solve and explain! Thanks!!

Problem 4: Shown below are four spring-cart systsems that consist of a spring connected to a cart. All systems are shown with the cart located at the equilibrium position. The cart is resting on a horizontal frictionless surface. If the cart is pulled to the right a small distance and released, the mass will oscillate back and forth. The amplitude of oscillation, mass of the cart and spring constants for the four cases are provided in the figure. Rank the cases shown based on their frequency of oscillation from greatest to least A Amplitude A B Amplitude A/2 C Amplitude A DAmplitude A 2M

Explanation / Answer

Angular frequency of the oscillation,

w = root(k/m)

Frequency, f = (1/2*pi)*root(k/m)

For

A. f1=(1/2*pi)*root(k/M)

B. f2=(1/2*pi)*root(k/M)

C. f3=(1/2*pi)*root(k/2*M)

D. f4=(1/2*pi)*root(k/2*M)

Rank based on thier frequency of oscillation from greatest to least:

A=B>C+D

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