What Is the Acceleration of a Mass in Simple Harmonic Motion?

[physgrl]

Homework Statement

A 0.2 kg object is suspended from a spring with a spring constant of k=10 N/m and is undergoing simple harmonic motion. What is its acceleration of the object at the instant when it is -0.05 m away from equilibrium?

A. 1000 m/s2
B. 40 m/s2
C. 0.1 m/s2
D. 2.5 m/s2

Homework Equations

F=ma
F=-kx
F=mg

The Attempt at a Solution

F=F(gravity)+F(spring)
ma=mg+(-kx)
0.20kg*a=(0.20kg*9.81m/s^2)+(-(10N/m*-0.05m))
a=12.31m/s^2

The answer is supposed to be D

 

[BruceW]

Yeah, this is a tricky question if you don't already know the answer.

The equilibrium point will shift due to the gravity force, so when the object is -0.05m away from equilibrium, this will not be the value of x.

To calculate the new equilibrium point, just solve for a=0. And then you can get the value of x which is -0.05m from the equilibrium point.

 

[gneill]

Yeah, this is a tricky question if you don't already know the answer.

The equilibrium point will shift due to the gravity force, so when the object is -0.05m away from equilibrium, this will not be the value of x.

Sure it will, if x is the displacement from equilibrium.

 

[gneill]

A straightforward way to approach this problem is to use write an expression for the position versus time (use a sine or cosine function). Find the corresponding acceleration expression (a touch of simple calculus). Take the position expression and rearrange for an expression for t in terms of x. Use it to find acceleration in terms of x.

 

[BruceW]

Sure it will, if x is the displacement from equilibrium.

I was referring to her/his? equations, where x is not the displacement from equilibrium. Your post isn't very helpful.

A straightforward way to approach this problem is to use write an expression for the position versus time (use a sine or cosine function). Find the corresponding acceleration expression (a touch of simple calculus). Take the position expression and rearrange for an expression for t in terms of x. Use it to find acceleration in terms of x.

Yep, that's another way of doing it.