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CHECK YOURSELF ANSWERS
1The period is 0.80 s and the frequency is 1.25 Hz.
2It will increase by the square root of 4, i.e. 2.
3It will decrease by the square root of 4, i.e. 2.
4
5The shift is 0.25 s and the period is 2.0 s so the phase difference is Ï=Â shiftÂ TÃ2Ï=0.252.0Ã2Ï=Ï4 or 45Â°.
6aiZero
ii0.20 m
bx=0.20sin(2Ï1.5t+Ï2)=0.20sin(4Ï3t+Ï2)=0.20cos(4Ï3t).
7Comparing with x = x0 sin(Ït) we find Ï=Ï3 and T=2ÏÏ=2ÏÏ3=6.0Â s.
8vmax=Ïx0Â andÂ amax=Ï2x0Â soÂ amaxvmax=Ï2x0Ïx0=Ï=2ÏT. So T=2Ïvmaxamax=2ÏÃ4.08.0=3.1Â s.
9The potential energy is 2.0 J and the total energy is 8.0 J so the kinetic energy is 6.0 J.
10A sine graph as shown, or a negative sine graph with period 1 s.

