Simple Harmonic Motion of a 2kg particle

[chewytess]

Homework Statement

A 2kg particle undergoes simple harmonic motion according to x=1.5sin((pi*t/4) + Pi/6)

A)What is the total mechanical energy of the particle?
B) Shortest time for particle to go from x=.5m to x=-.75m

Homework Equations

Potential energy=.5kx^2

The Attempt at a Solution

I don't get what to use for k or x to find the total energy. Please help?

 

[rock.freak667]

The general equation for SHM is x=Asin(ωt+Φ). The total energy is a sum of the KE and PE of the system (which are interchanged as time passes). So when KE increase, PE decreases and vice versa.

So what happens when the PE reaches zero, shouldn't the KE reach the maximum value (the total energy of the system)?

I think you know KE = ½mv² and v= dx/dt.

 

[Mike Pemulis]

I don't get what to use for k or x to find the total energy. Please help?

k and x only give you the potential energy, right? But the total energy is kinetic energy plus potential energy,

E = KE + PE

How do we deal with kinetic energy?

Edit to include this:

I think you know KE = ½mv2 and v= dx/dt.

I don't think that's right right way to go here. OP might not know enough calculus yet, and you can do the problem without it.

 

[chewytess]

I know that the kinetic energy plus the potential energy is equal to the totalt energy. I know the easiest way to solve the problem would just be to find one of them at the max. I am just confused on which one to solve for and how. My teacher did a really bad job on explaning this chapter and I am just trying to get some insight on this to help me better understand. Thnx

 

[rock.freak667]

I know that the kinetic energy plus the potential energy is equal to the totalt energy. I know the easiest way to solve the problem would just be to find one of them at the max. I am just confused on which one to solve for and how. My teacher did a really bad job on explaning this chapter and I am just trying to get some insight on this to help me better understand. Thnx

You'll either have at max:

KE_max = 0.5mv²

OR

PE_max = 0.5kx²

with the constraints of the problem being either given m or k, which do you think you should use?

 

[chewytess]

I think i should find the max pe. I am just confused on what numbers to use

 

[Mike Pemulis]

So, like you said we need k and x.

1. Maximum PE means maximum x, right? What's the maximum x-value? If you're stuck, try graphing your equation from the first post.

2. k is related to the frequency of the oscillator. This should make some sense; a stiffer spring will oscillate quicker. Your book should have an equation that relates the period (or frequency) of the motion to the spring constant of the spring.

 

[chewytess]

Thank you it finally clicked, your help is much appreciated!