Defining period (T) in terms of A(max) and V(max)

• Apr 5, 2004

• #1

new324

30

0

Hello, it's me again. Yes Physics is most of my life right now. :tongue: Here's one I'm not sure how to complete. Any hints/tips would be well appreciated. Thank You!

An object executing simple harmonic motion has a maximum speed v(max) and a maximum acceleration a(max). Find (a) the amplitude, A, and (b) the period, T, of this motion. Express your answers in terms of v(max) and a(max).

Well first I know I'm going to use the a(max) and v(max) formulas (duh ).

a(max)= Aω^2
v(max)=Aω

Well (a) is pretty cut and paste. Squaring v(max) yields A^2*ω^2
Put this over a(max), and the ω^2's cancel and the square of A cancels as well. So A= v(max)^2 / a(max)

Part (b) I'm having a little trouble finding the suitable equation to use. I thought about using, a= -ω^2*A*Cos(ωT). From here I saw a(max) cancels Aω^2 leaving -Cos(ωT)=1. However, only numbers (or radians) and a(max), v(max) can be used in the final solution. Any hints/tips? Much obliged!

 

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• Apr 5, 2004

• #2

Doc Al

Mentor

45,569

2,219

[tex]T = \frac{2 \pi}{\omega}[/tex]

 

• Apr 5, 2004

• #3

new324

30

0

Of course! Lol. It's always the easiest things I overlook. Thank You!

-The Village Idiot

 

1. What is the definition of period (T)?

The period (T) is the time it takes for one complete cycle or oscillation to occur. It is measured in seconds.

2. How is period (T) related to A(max) and V(max)?

In a simple harmonic motion, the period (T) is directly proportional to the amplitude (A) and inversely proportional to the maximum velocity (V). This means that as the amplitude increases, the period also increases, while a higher maximum velocity results in a shorter period.

3. What is the formula for calculating period (T) in terms of A(max) and V(max)?

The formula for period (T) is T = 2π(A/V), where A is the amplitude and V is the maximum velocity.

4. How can period (T) be measured experimentally?

Period (T) can be measured experimentally by using a stopwatch to time the number of oscillations that occur in a given time period. The period can then be calculated by dividing the time by the number of oscillations.

5. Can period (T) vary for different types of oscillations?

Yes, the period (T) can vary for different types of oscillations. It depends on factors such as the mass and stiffness of the object, as well as the presence of any external forces. For example, the period of a pendulum will be different from the period of a spring.