I'm really having a hard time determining an equation for a pendulum problem. It has to be in the form H(t)=asin[b(t-c)]=d. I've already determined a=25, d=30 and b=pi/14 but I can't figure out how to get c (the phase shift). How do I figure out the phase shift in these type of problems? Thanks!!!
To determine the phase shift 'c' in a pendulum problem, you need to use the given information and equations to solve for it. Here's how you can do it:
1. Start with the equation for the pendulum problem: H(t) = asin[b(t - c)] = d.
2. Plug in the given values:
- a = 25
- d = 30
- b = π/14
The equation becomes:
30 = 25sin[(π/14)(t - c)]
3. Divide both sides of the equation by 25 to isolate the sin[(π/14)(t - c)] term:
30/25 = sin[(π/14)(t - c)]
4. Simplify the equation:
6/5 = sin[(π/14)(t - c)]
5. To solve for the phase shift 'c', take the inverse sine (sin⁻¹) of both sides of the equation:
sin⁻¹(6/5) = sin⁻¹[sin[(π/14)(t - c)]]
6. Use the fact that sin(sin⁻¹(x)) = x:
sin⁻¹(6/5) = (π/14)(t - c)
7. Solve for 'c' by isolating it:
c = t - (14/π)sin⁻¹(6/5)
And that's how you determine the phase shift 'c' in a pendulum problem. Plug in the given values of 't' and calculate 'c' using the equation derived in step 7.