Finding Period and Angular Frequency in Simple Harmonic Motion

[Jimmy84]

Homework Statement

a particle moves to the right along the x-axis with a simple harmonic motion from x0 = 3.0cm in t=0 . if its position x is given by x = 4.0 cos (pi t + phi) , in cms ; find its period T.

Homework Equations

The Attempt at a Solution

The problem ask me more things like the aplitude, phi and others but the amplitude i found was 4.0cm and phi was 41.1 . Now I am stuck because I am asked more things such as the angular frequency and more the equtions for the velocity , acceleration and more but I need T or omega in order to find those. How can I find T?

My guess is that the problem already suggests T but I am starting to learn about harmonic motion so I don't see things clearly for now can anyone give em soem help in order to find T or the angualr frecuency ?

Thanks lot in advance.

 

[PeterO]

Homework Statement

a particle moves to the right along the x-axis with a simple harmonic motion from x0 = 3.0cm in t=0 . if its position x is given by x = 4.0 cos (pi t + phi) , in cms ; find its period T.

Homework Equations

The Attempt at a Solution

The problem ask me more things like the aplitude, phi and others but the amplitude i found was 4.0cm and phi was 41.1 . Now I am stuck because I am asked more things such as the angular frequency and more the equtions for the velocity , acceleration and more but I need T or omega in order to find those. How can I find T?

My guess is that the problem already suggests T but I am starting to learn about harmonic motion so I don't see things clearly for now can anyone give em soem help in order to find T or the angualr frecuency ?

Thanks lot in advance.

The period refers to the length of time from when something happens, to what it happens the next time.

What value of t gives a maximum x value?
What next value of t will also give the maximum x value?
the difference in those two is the period.

Note we use an extreme value, since the particle undergoing SHM is at each intermediate position twice during a cycle - but traveling in the other direction.