High School

In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression [tex]x = 6.00 \cos(t \cdot \frac{\pi}{4})[/tex]. What is the amplitude of the oscillation?

1) 3.00
2) 4.00
3) 6.00
4) 8.00

Answer :

The amplitude of the piston's oscillation, determined from the given expression x = 6.00 cos(t * π/4), is 6.00 units.

The correct answer is option 3.

Certainly, let's go through the detailed calculation step by step:

The expression for the piston's position is given as x = 6.00 cos(t * π/4).

In simple harmonic motion (SHM), the general form of displacement is x = A cos(ωt + φ), where:

A is the amplitude,

ω is the angular frequency,

t is time, and

φ is the phase constant.

Comparing the given expression with the general form of SHM, we can identify the amplitude (A):

A = 6.00

Therefore, from the given options the correct one is 3.