Springs and simple harmonic motion

In summary, the conversation discussed solving for the magnitude of acceleration at a specific time for a mass oscillating on a spring with a given period and initial position. The process involved converting the period to angular velocity, solving for the amplitude of the oscillation using the given initial position, and then plugging in all values into the equation for acceleration. The mistake made was forgetting to convert the amplitude from centimeters to meters before computing the final answer.
  • #1
Jm4872
12
0

Homework Statement



A mass is oscillating on a spring with a period of 1.45 s. At t = 0 the mass has zero speed and is at x = 8.80 cm. What is the magnitude of the acceleration at t = 2.30 s?

Homework Equations


x(t)=Acos(wt + phi)
a(t)=-Aw^2cos(wt + phi)
a=w^2x
T=2pi/w


The Attempt at a Solution



I've tried this a few different ways, first off what I do is convert the period (1.45s) to angular velocity using T=2pi/w, this then gives me the result of 4.33 rad/s. Using this I then substitute values into the equation for position to get,
8.80 = Acos(0)
from this equation I then solve for A and receive 8.80 cm.
Now the information I have is..
w=4.33 rad/s
A=8.80cm
t=2.30s
All of this I put into my equation for acceleration to get..
a(2.30)=-8.80(4.33^2)cos(4.33*2.30)
solving for acceleration the result comes to be 142 m/s^2, however when I input this number it comes out to be wrong? I'm confused as to what it is that I'm doing wrong, please help!
 
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  • #2
You just forgot to convert the amplitude of the oscillation (which is in cm) to metres before computing your answer.
 
  • #3
oh wow haha now I feel dumb!
haha thank you!
 

Related to Springs and simple harmonic motion

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth in a straight line with a constant frequency and amplitude, such as a mass attached to a spring.

2. How do springs create simple harmonic motion?

When a spring is stretched or compressed, it exerts a force that is directly proportional to the displacement of the object attached to it. This force causes the object to oscillate back and forth, creating simple harmonic motion.

3. What is the relationship between mass and spring constant in simple harmonic motion?

The period of a mass-spring system, or the time it takes for one complete cycle of motion, is directly proportional to the square root of the mass and inversely proportional to the spring constant. This means that a larger mass or a stiffer spring will result in a longer period of oscillation.

4. How does amplitude affect simple harmonic motion?

The amplitude, or the maximum displacement from the equilibrium position, does not affect the period of simple harmonic motion. However, a larger amplitude will result in a greater maximum speed and acceleration, and therefore a greater amount of energy being transferred between kinetic and potential energy.

5. Can simple harmonic motion occur without a spring?

Yes, simple harmonic motion can occur in other systems besides a mass-spring system. Any system that follows Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement, can exhibit simple harmonic motion. Examples include pendulums and vibrating strings.

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