# What Is the Smallest Value of Time t for This Simple Harmonic Motion?

• PolarClaw
In summary, the conversation is about finding the smallest value of time t in a particle's simple harmonic motion, given its initial velocity and velocity at a later time. The position and speed equations for simple harmonic motion are mentioned, and the conversation ends with the person finding the solution to their problem.
PolarClaw
Hi,

I've been stuck on trying to figure out what I am not seeing in the problem as i just can't seem to get the answer.

A particle moving in simple harmonic motion with a period T = 1.5s passes through the equilibrium point at time t initial = 0 with a velocity of 1.0m/s to the right. At a time t later, the particle is observed to move to the left with a velocity of 0.50m/s. What is the smallest value of the time t?

I just can't see what to do (although i have calculated the angular frequency ( 4(pi)/3).

PolarClaw said:
Hi,

I've been stuck on trying to figure out what I am not seeing in the problem as i just can't seem to get the answer.

A particle moving in simple harmonic motion with a period T = 1.5s passes through the equilibrium point at time t initial = 0 with a velocity of 1.0m/s to the right. At a time t later, the particle is observed to move to the left with a velocity of 0.50m/s. What is the smallest value of the time t?

I just can't see what to do (although i have calculated the angular frequency ( 4(pi)/3).
The position of the particle will be:

$$x = A_0sin(\omega t + \phi)$$

Given the initial condition, x = 0 at t = 0, $\phi = 0$

The speed is given by:

$$\dot x = -A_0\omega cos(\omega t) = v_0cos(\omega t)$$

If $\dot x(t_1) = v_1 = -.5v_0$, then what is $cos(\omega t_1)$?

So from that, you should be able to work out t1.

AM

ahh, i had tried that but i differetiated wrong got the answer now thanks.

## 1. What is harmonic motion?

Harmonic motion refers to the repetitive back and forth movement of an object around a central equilibrium point. It is characterized by a constant period and amplitude.

## 2. What causes an object to experience harmonic motion?

Harmonic motion is caused by a restoring force, such as gravity or a spring, that pulls the object back towards its equilibrium position when it is displaced from it.

## 3. How is harmonic motion related to simple harmonic oscillation?

Harmonic motion and simple harmonic oscillation are essentially the same thing. They both describe the motion of an object that is oscillating back and forth with a constant period and amplitude.

## 4. What factors affect the period of a harmonic motion?

The period of harmonic motion is affected by the mass of the object, the strength of the restoring force, and the initial displacement from the equilibrium position.

## 5. How is harmonic motion used in real life?

Harmonic motion is used in many real-life applications, such as pendulum clocks, musical instruments, and even car suspensions. It is also used in science and engineering to model and analyze various systems.

• Introductory Physics Homework Help
Replies
51
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
856
• Introductory Physics Homework Help
Replies
13
Views
311
• Introductory Physics Homework Help
Replies
17
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
846
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
864
• Introductory Physics Homework Help
Replies
3
Views
2K