Write a sine function for the following problem: 1. A particle starts at rest. At time = 0 h(t) = 0 and the particle begins to oscillate between a height of 5 in and - 5 in. It
reaches its maximum height after 2.5 seconds and a minimum height after 7.5 seconds. Sketch a graph of the system
and write a sinusoidal equation that models this harmonic motion.

1. Amplitude (a) = in
2. Vertical shift (d) = _ in.
3. Period (P) = _sec.
4. Frequency (f) =__cycles/sec (Write as a fraction)
5. w=
rads/sec (Write as a fraction. Use pi for 7)
6. h(t) = _ _sin(t)

amplitude A = 5

vertical shift = 0

period T = 10 s

frequency = 1/T = 0.1 Hz

angular frequency ω = π/5

h(t) = 5sin(πt/5)

Step-by-step explanation:

An oscillator cannot move between ± 5 units, be at rest at t=0 and at maximum 2.5 s later without some serious external acceleration being applied. It just does not work.

I will ASSUME that the particle is at maximum velocity at t = 0 and use the remaining inputs as stated

As h(0) = 0 the Sine function fits nicely as sin0 = 0

A = 5 as the particle swings between +5 and -5

h(t) = 5sin(ωt)

ω will have units of rad/s

We know the particle will move from max to min position in half the period.

so the period T = 2(7.5 - 2.5) = 10 s

There are 2π radians in each cycle, therefore

ω = 2π rad/10 s = π/5 rad/s

h(t) = 5sin(πt/5)

y=mx+b is the final answer!   : )

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step-by-step explanation: