## SHM Lab

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1. Parameter A

To change A to .10 m, we had to change the initial displacement from equilibrium to .10 m (so A is the amplitude of the motion). Given the equation y = Asin(Bt+C) + D, this makes sense, because sin has a range of [-1, 1], so Asin has a range of [-A, A].

2. Parameter D

To get D equal to -.05 m, we had to change the y-value of the equilibrium position to -.05 m (by zeroing the sensor when the object was .05 m above the equilibrium position). To make a graph symmetrical about the y-axis (D=0), we would have to zero the sensor when the object was at the equilibrium position.

3. Parameter C

In the initial setup, the sensor was configured to start recording data when the object passed the equilibrium point, so there was no offset. As a result, C was 0 (or 2π), which corresponds to no offset (or one complete cycle of offset, which is equivalent). To make C equal to π/2, we had to start collecting data one fourth of the way through the cycle (at the top if the cycle started at 0 with the object moving up). To make C equal to π, we would have had to start collecting data at the halfway point of the cycle (at the equilibrium position with the object moving downward).

4. Parameter B

If B = 6.28 (= 2π), then given B = 2π/T, T = 2π/B = 1 second. To double B, since B = ω = sqrt(k/m), the mass would have to be reduced by a factor of four—sqrt(k/(.25m)) = sqrt(4k/m) = 2sqrt(k/m) = 2B.

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