What Is the Displacement and Acceleration at 2 Seconds in SHM?

[Pho3nix]

Homework Statement

A SHM motion can be described by a=-400x. The amplitude is 8cm. Find the displacement and acceleration at a time of 2s.

Homework Equations

x = A sin(2pi f t)
x = A cos(2pi f t)
a=-(2pi f)squared*x

The Attempt at a Solution

Firstly I realized that 400=2pi f , so f =64Hz. But then I go stuck cos you don't know if this is a cos or sin oscillation. I am not sure where to go from here, but I just know there's a way around this.

Any help?

 

[anathema]

Thank you for your post. It is great to see that you are working on understanding SHM motion. Let me help you with your problem.

First, let's start by understanding what the equation a = -400x represents. This is the equation for acceleration in SHM, where a is the acceleration, x is the displacement, and 400 is the angular frequency squared. This means that the frequency of the oscillation is 64 Hz, as you correctly calculated.

Next, we need to determine whether the motion is described by a cosine or sine function. This can be done by looking at the initial conditions of the problem. In this case, we are given the amplitude, which is 8 cm. This means that the displacement at time t = 0 is either 8 cm or -8 cm, depending on whether the motion starts from the equilibrium position or from the extreme position. For simplicity, let's assume that the motion starts from the equilibrium position, so the displacement at t = 0 is 0 cm and the motion is described by a cosine function.

Now, we can use the equation x = A cos(2pi f t) to find the displacement at a time of 2 s. Plugging in the values, we get:

x = 8 cm * cos(2pi * 64 Hz * 2 s)

Solving this equation, we get x = 8 cm * cos(256pi) = 8 cm. This means that the displacement at t = 2 s is 8 cm.

Finally, we can use the equation a = -(2pi f)^2 * x to find the acceleration at t = 2 s. Plugging in the values, we get:

a = -(2pi * 64 Hz)^2 * 8 cm = -32768 cm/s^2

Therefore, the displacement at t = 2 s is 8 cm and the acceleration is -32768 cm/s^2.

I hope this helps you understand SHM motion better. Keep up the good work!

 

[Moetasim]

Hello, thank you for reaching out. It seems like you are on the right track. Since the equation given is a=-400x, the SHM motion can be described by x = A cos(2pi f t), where A is the amplitude and f is the frequency. In this case, the amplitude is 8cm and the frequency is 64Hz.

To find the displacement at a time of 2s, we can plug in the values into the equation: x = 8 cos(2pi * 64 * 2) = 8 cos(256pi) = 8.

To find the acceleration at a time of 2s, we can use the formula a=-(2pi f)^2*x. Plugging in the values, we get a=-(2pi*64)^2*8 = -204800x.

So the displacement at 2s is 8cm and the acceleration is -204800x. I hope this helps. Remember to always check your units and make sure they are consistent throughout the problem. Good luck with your homework!