# Time it takes an oscillating mass to reach a certain velocity

• Terp
In summary, the conversation revolves around a problem related to simple harmonic motion. The equation for the velocity of an object in this type of motion is given, and the goal is to find the first time when the velocity is a specific value. The conversation includes attempts at solving the problem and discussions about the periodic nature of trigonometric functions. The final answer is around -0.12 seconds after t=0s.
Terp
Hi everybody, this problem is giving me trouble and I was wondering if you could give me any advice.

## Homework Statement

The velocity of an object in simple harmonic motion is given by vx(t)= - (0.35 m/s)sin(20t + pi), where t is in s.

What is the first time after t=0s at which the velocity is - 0.25 m/s?

## Homework Equations

See the equation above.

## The Attempt at a Solution

I simply plugged -.25 m/s in for vx(t) above and solved for t, so I got:

-0.25 = -0.35sin(20t + pi)
.714 = sin(20t + pi)

When I solve for t I get t = -.397e-1 = -.0397s, but mastering physics (the program I use to do homework online) say it's wrong. I entered the answer as positive. Anybody have any idea? Thanks a lot!

edit: I just went to see my professor and he helped me set it up, when finished we had sin(20t) = -5/7, but master physics says it's wrong.

Last edited:
Trigonometric functions are periodic. This means that the function "repeats" itself over and over as you move along the X axis. If you visualize the sine involved in your problem, you'll realize that if you move sufficiently far to the right from -.0397 (and beyond 0), you'll get at a point p where vt(p) = vt(-.0397). That point is in fact -.0397 + Pi/10, because Pi/10 is the period of vt(x).

Thanks for the reply. Does that mean that the time it reaches -.25m/s is .275? (-0.397 + pi/10). Where did that 10 come from? Thanks!

The period of a sine function is given by 2pi/k, where k is the coefficient of x inside the bracket (i.e. for vt(x), the coefficient is 20). Really, it's not very useful for you to hear about this from me. You'd be better off learning better about trigonometric functions.

I believe that I do have a decent understand of trigonometric functions, I just can't figure out why this problem is giving me so much trouble. I can't be doing much wrong...]

I've got a graph of the wave drawn out and where the time will fall on the wave, but I just can't get it numerically.

Last edited:
But you just did; .275 s.

Thanks for the reply, but this darn program say it's wrong. I really don't like doing homework online.

Did you calculate arcsine in radians?

Yeah, arcsine(5/7) is .7956, then multiplying that my (1/20) as by my answer in the first post gives .0397

Yeah, arcsine(5/7) is .7956, then multiplying that my (1/20) as by my answer in the first post gives .0397

You forgot to subtract pi before dividing by 20.

Calculating it myself, I get around -0.12 for t. -0.12 + pi/10 = 0.2, approximately.

Thanks a lot for the help, Werg. Any more input from anybody would be appreciated!

## 1. How does the mass of an object affect the time it takes to reach a certain velocity?

The mass of an object has a direct impact on the time it takes to reach a certain velocity. Objects with a larger mass will require more force to accelerate to a certain velocity, resulting in a longer time to reach that velocity compared to objects with a smaller mass.

## 2. Does the type of oscillation affect the time it takes to reach a certain velocity?

Yes, the type of oscillation can affect the time it takes for an object to reach a certain velocity. For example, an object that is oscillating in a simple harmonic motion will reach its maximum velocity faster than an object oscillating in a damped harmonic motion.

## 3. What role does the amplitude of oscillation play in the time it takes to reach a certain velocity?

The amplitude of oscillation does not have a significant impact on the time it takes to reach a certain velocity. As long as the amplitude is small enough to maintain the object's motion within the linear range, the time to reach a certain velocity will remain constant.

## 4. How does the initial velocity of an object affect the time it takes to reach a certain velocity?

The initial velocity of an object does not affect the time it takes to reach a certain velocity. The time it takes for an object to reach a certain velocity is solely dependent on the magnitude of the acceleration and the distance traveled.

## 5. Can the time it takes for an object to reach a certain velocity be calculated mathematically?

Yes, the time it takes for an object to reach a certain velocity can be calculated using the equation t = √(2d/a), where t is the time, d is the distance traveled, and a is the magnitude of acceleration. This equation assumes that the initial velocity is 0 and that the object is moving in a straight line with constant acceleration.

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