The equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is below. At which times will the spring be at a height of 12 in. above equilibrium? Select all that apply.

Question

h = -15sin (pi/3 t)

B) 2.1
D) 11.1
E) 12.8

Answer 1

We can start by setting h = 12 and solving for t using the given equation:

12 = -15sin(pi/3 t)

Dividing both sides by -15 and taking the inverse sine, we get:

sin^-1(-12/15) = pi/3 t

Simplifying, we get:

t = (3/2) sin^-1(-4/5)

Using a calculator, we find that:

sin^-1(-4/5) = -53.13 degrees

t = (3/2)(-53.13 degrees)/(180 degrees/pi)

t = 2.1 or 11.1 seconds

Therefore, options B and D are correct. Option E is not correct as it corresponds to a height of -12 inches below equilibrium, not 12 inches above.