More Simple Harmonic Oscillations

• ubbaken
In summary: Just use the same method to solve for the phase and then use that phase to solve for the velocity at the given time. In summary, two problems involving simple harmonic motion were discussed. The first involved finding the time it takes for an object to move from a certain position to another, given its period and amplitude. The second problem asked for the first time at which the velocity of an object reaches a certain value, using a given equation. The key to solving these problems is finding the phase constant and using it to solve for the desired quantity.
ubbaken
An object in simple harmonic motion oscillates with a period of 4.00 s and an amplitude of 9.08 cm. How long does the object take to move from x=0.00 cm to x=5.07 cm?

I set up my eqn like this: 0.0908cos(ωt)=0.0507
cos(ωt)=0.583
ωt=56.1
then with ω=90deg I get 0.623s which is slightly higher than I think the answer would be, and is ultimately incorrect.

I've tried working the problem out a number of times, in rad and degs to make sure I'm not making an error there, and I get the same answer.

The velocity of an object in simple harmonic motion is given by v(t)= -(0.250 m/s)sin(17.0t + 1.00π), where t is in seconds. What is the first time after t=0.00 s at which the velocity is -0.120 m/s?

for this one it seems like I just have to work it through to find t. When I do so, I get down to 17.0t+1.00π=28.7 (from using sin^-1=-.120/-.250) and then there is no answer that fits (0<t<5 approx.). Plus, in trying the answers, they are wrong.

I'm pretty spent on these, any and all help would be appreciated.

Last edited by a moderator:
You have two condtions x(0)=0, and x(t)=5.07cm. To use the equation that $$x(t)=Acos(\omega t + \phi)$$ you have to first find the phase constant. So you need to make a statement like
$$x(t)=Acos(\omega t + \phi)=0$$

It is pretty obvious for this one because you essentially want to just start with a sine function. But you can solve and find the phase. Then you want to use that phase you found to solve when $$x(t)=Acos(\omega t + \phi)=5.07cm$$. Another problem I see with what you did is you are saying the angular frequency has units of degrees? Remember that $$\omega = \frac{2 \pi}{T}$$ where T is the period, and has units of s^-1.

The second one is very similar, if you can get the first one then you can get the second one.

Thank you for your post, but I'm not sure what you're asking for exactly. Are you looking for an explanation of how to solve these problems or are you asking for help with specific steps in your calculations? Can you provide more information about what you've tried and what you're having trouble with?
In general, for the first problem, you can use the equation x(t) = A*cos(ωt) to solve for the time when the object is at x = 5.07 cm. Plugging in the given values, you can solve for ωt and then divide by ω to get the time. Make sure you are using the correct units for ω (radians/second or degrees/second).

For the second problem, you have the equation for velocity, so you can set it equal to -0.120 m/s and solve for t. Make sure you are using the correct units for t (seconds). It might be helpful to graph the velocity equation and see where it crosses -0.120 m/s to get an idea of what values of t you should expect.

I hope this helps. If you are still having trouble, please provide more information and I will try my best to assist you.

1. What is a simple harmonic oscillator?

A simple harmonic oscillator is a system that exhibits periodic motion where the restoring force is proportional to the displacement from the equilibrium position. This means that as the system moves away from its equilibrium position, it experiences a force that pulls it back towards the equilibrium position.

2. What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A cos(ωt + φ), where x represents the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase constant.

3. How does the mass of an object affect simple harmonic motion?

The mass of an object does not affect the frequency of simple harmonic motion, but it does affect the amplitude. A larger mass will result in a smaller amplitude, and a smaller mass will result in a larger amplitude.

4. What is the relationship between period and frequency in simple harmonic motion?

The period of a simple harmonic oscillator is the time it takes for one complete cycle of motion, while the frequency is the number of cycles per unit time. The relationship between the two is T = 1/f, where T is the period and f is the frequency.

5. Can simple harmonic motion occur in all types of systems?

Yes, simple harmonic motion can occur in all types of systems, as long as there is a restoring force that is proportional to the displacement from equilibrium. This includes systems such as pendulums, mass-spring systems, and even atomic vibrations.

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