# Spring constant of object in simple harmonic motion

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1. Nov 28, 2015

### qlzlahs

1. The problem statement, all variables and given/known data
A 15.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by y(t)=4.50 cos[(19.5s−1)t−π/8] in centimeters.
What is the spring constant of the spring?

2. Relevant equations
y component of spring force = -k*displacement = mg
k = (mg)/displacement

3. The attempt at a solution
I thought the spring constant of the spring was basically (mg)/displacement. mg = 15 N, and the total displacement of the spring is 4.50*2 = 9.00 centimeters. I thought the spring constant was 15N/0.09m = 166.67 N/m.

2. Nov 28, 2015

### TSny

Hello, and welcome to PF!
This formula for the spring constant applies to the situation where the mass is hanging at rest. The displacement here would be the amount the spring is stretched while hanging at rest. This displacement is not related at all to the 4.50 cm amplitude of oscillation. Since you are not given the amount that the spring is stretched if the mass is hanging at rest, you will not be able to get the spring constant this way.

Do you know any relation between the spring constant and the period or frequency of oscillation?

3. Nov 28, 2015

### Staff: Mentor

Hi qlzlahs, Welcome to Physics Forums.

I presume that your equation for the displacement as a function of time, y(t)=4.50 cos[(19.5s−1)t−π/8] was meant to be

y(t)=4.50 cos[(19.5s−1)t−π/8]

so that the units of the argument of the cosine would make sense?

Note that the relationship between displacement and weight of the mass on a spring applies to the static case when there's no motion -- the mass is hanging motionless. In that case the mass is stationary at an equilibrium position, where the weight is equal to the force that the spring provides.

Unfortunately you aren't given information about this equilibrium scenario. Instead you are given information for oscillations about the equilibrium.

So, look into your text and class notes (or on the web) for information on the period or frequency of mass-spring oscillation. You should find that it is related to the spring constant. Can you pick out the oscillation frequency from your displacement formula?

Edit: Ah. I see that TSny got there before me. Oh well, carry on...

4. Nov 28, 2015

### TSny

Please feel free to continue contributing to this thread!

5. Nov 28, 2015

### qlzlahs

I found that omega equals the square root of (k/m), and used it to find the answer. Thank you both!