To calculate the motion of an object undergoing simple harmonic motion (SHM) with an amplitude of 3 cm and a frequency of 30 Hz, you can use the following formulas:
- Period (T): The time taken for one complete oscillation.
T = 1 / f
where f is the frequency.
In this case, the frequency is given as 30 Hz. Therefore:
T = 1 / 30 Hz = 0.0333... seconds (approximately)
- Angular frequency (ω): The rate of change of angle or phase in SHM.
ω = 2πf
where f is the frequency.
In this case, the frequency is given as 30 Hz. Therefore:
ω = 2π × 30 Hz = 60π radians per second
- Displacement as a function of time (x(t)):
x(t) = A * sin(ωt)
where A is the amplitude, ω is the angular frequency, and t is the time.
In this case, the amplitude is given as 3 cm, and the angular frequency is 60π radians per second. Therefore:
x(t) = 3 cm * sin(60πt)
These equations allow you to calculate the displacement of the object as a function of time during its simple harmonic motion. You can substitute different values of time (t) into the equation to find the corresponding displacement at that time.