• Support PF! Buy your school textbooks, materials and every day products Here!

Simple Harmonic Motion of a 2kg particle

  • Thread starter chewytess
  • Start date
  • #1
9
0
1. 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

2. Homework Equations
Potential energy=.5kx^2
3. The Attempt at a Solution

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

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
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.
 
  • #3
120
0
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.
 
  • #4
9
0
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 im just trying to get some insight on this to help me better understand. Thnx
 
  • #5
rock.freak667
Homework Helper
6,230
31
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 im just trying to get some insight on this to help me better understand. Thnx
You'll either have at max:

KEmax = 0.5mv2

OR

PEmax = 0.5kx2

with the constraints of the problem being either given m or k, which do you think you should use?
 
  • #6
9
0
I think i should find the max pe. Im just confused on what numbers to use
 
  • #7
120
0
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.
 
  • #8
9
0
Thank you it finally clicked, your help is much appreciated!!
 

Related Threads for: Simple Harmonic Motion of a 2kg particle

  • Last Post
Replies
1
Views
812
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
9
Views
5K
  • Last Post
Replies
1
Views
3K
Replies
5
Views
3K
Replies
1
Views
2K
  • Last Post
Replies
3
Views
2K
Top