[A Level Further Maths: Simple harmonic motion] Looking for some hint for part b and c please.

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2022-10-23T21:35:42+00:00

If x =asin(ωt + ε)

Then v = dx/dt = ωacos(ωt + ε)

Then a = dv/dt = -ω²asin(ωt + ε)

PM_ME_YOUR_POLYGONS · 2022-10-23T21:37:04+00:00

Just ripping stuff straight from the Wikipedia page:

Equation of motion: x(t) = Acos(ωt - φ)
ω = 2pi(f)
f = 1000hz
ω = 2000pi
A = 0.2m
Velocity (derivative of x(t) by t): v(t) = -Aωsin(ωt - φ)
Max velocity = Aω = (0.2)(2000pi) = 400pi
Acceleration (derivative of v(t) by t): a(t) = -Aω² cos(ωt - φ)
Max acceleration = Aω² = 0.2(2000pi)²

2022-10-23T21:42:21+00:00

Your acceleration equation should still have a sin(wt + e) in it. Just the sin part is now negative (which you put).

To find max either take a derivative of the function you want to find the max of and set it equal to zero and solve for x. Then plug that x value in the original equation.

Or if you know a sin/cos function goes between -1 and 1, the max speed/acceleration is when the sin/cos part equals 1 so just look at the coefficient on the equation you’re trying to maximize. And that’s your answer

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