Displacement in simple harmonic motion

Any motion that repeats at regular intervals is called periodic, or harmonic, motion. Simple harmonic motion is a particular type of repeated motion that is a sinusoidal function of time.

Note:

1. This law is also applicable for any physical quantity that changes its value in a repeating harmonic manner, therefore any_quantity is used.

Links:

1. Wikipedia.

displacement

Displacement from rest, usually a function of time. See any_quantity.

Symbol:

q

Latex:

\(q\)

Dimension:

any_dimension

amplitude

The maximum absolute value of the displacement. See any_quantity.

Symbol:

q_max

Latex:

\(q_\text{max}\)

Dimension:

any_dimension

angular_frequency

angular_frequency of oscillations.

Symbol:

w

Latex:

\(\omega\)

Dimension:

angle/time

phase_shift

phase_shift of oscillations, which is the phase at \(t = 0\).

Symbol:

phi

Latex:

\(\varphi\)

Dimension:

angle

time

time at which displacement is measured.

Symbol:

t

Latex:

\(t\)

Dimension:

time

law

q = q_max * cos(w * t + phi)

Latex:

\[q = q_\text{max} \cos{\left(\omega t + \varphi \right)}\]