Question

A frictionless cart of mass M is attached to a spring with spring constant k. When the cart is displaced 6 cm from its rest position and released, it oscillates with a period of 2 seconds.Four English majors are discussing what would happen to the period of oscillation if the cart was displaced 12 cm from its rest position instead of 6 cm and again released.With which, if any, of these students do you agree?

Answer 1

Answer:

Time period of horizontal Oscillation  = T = 2$\pi$$\sqrt{\frac{m}{k} }$

As you can see, from the equation, Period of oscillation depends upon the mass and the spring constant. Not on the displacement.

Explanation:

Solution:

As we know that:

F = Kx

Here,

K = Spring constant

x = displacement.

First, they are displacing it with 6 cm from its rest position for which Time period of the oscillation is T = 2 seconds.

But next, they want to know the effect on the time period of the oscillation if the displacement x is doubled from 6cm to 12 cm.

First of all, let us see the equation of the time period of the oscillation.

We need to check, if time period does depend on the displacement or not.

As we know,

Time period of horizontal Oscillation  = T = 2$\pi$$\sqrt{\frac{m}{k} }$

As you can see, from the equation, Period of oscillation depends upon the mass and the spring constant. Not on the displacement.

Since, K is the constant for a particular spring, we need to change the mass of the cart to change the time period.

Hence the Time period will remain same.

Answer 2

The time period will remain the same in both conditions. The time period of horizontal Oscillation will be $2 \pi \sqrt{\frac{m}{k} }$.

What is the time period of oscillation?

The period is the amount of time it takes for a particle to perform one full oscillation. T is the symbol for it. Taking the reciprocal of the frequency yields the frequency of the oscillation.

From Hooke's law;

F = Kx

Where,

K is the spring constant

x is the  displacement

First, they move it 6 cm from its rest position, with a T = 2 second oscillation period.

However, they want to know what influence doubling the displacement x from 6 cm to 12 cm has on the oscillation's time period.

Let's start by looking at the oscillation's time period equation. We need to see if the time period is affected by the shift.

The time period of the horizontal oscillation is given by;

$\rm T = 2 \pi \sqrt{\frac{m}{k} }$

As the equation shows, the period of oscillation is determined by the mass and the spring constant. On the displacement, no.

We must modify the mass of the cart to change the time period since K is the constant for each spring.

Hence the time period will not change.

To learn more about the time period of oscillation refer to the link;

https://brainly.com/question/20070798