Question 19.WE.2: A pendulum oscillates with frequency 1.5 Hz and amplitude 0....

Step 1 Select the correct equation. In this case, the displacement is zero when t = 0, so we use the sine form:
x = x_{0} sin ωt
Step 2 From the frequency f, calculate the angular frequency ω:
ω = 2πf = 2 × π × 1.5 = 3.0π
Step 3 Substitute values in the equation: x_{0} = 0.10 m, so:
x = 0.10 sin (3.0πt)
Hint: Remember to put your calculator into radian mode

Step 4 To find x when t = 0.50 s, substitute for t and calculate the answer:
x = 0.10 sin (2π × 1.5 × 0.50)
= 0.10 sin (4.713)
= −0.10 m
This means that the pendulum is at the extreme end of its oscillation; the minus sign means that it is at the negative or left-hand end, assuming you have chosen to consider displacements to the right as positive.
(If your calculation went like this:
x = 0.10 sin (2π × 1.5 × 0.50) = 0.10 sin (4.713)
= −8.2 × 10^{-3} m

then your calculator was incorrectly set to work in degrees, not radians.)