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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 ϕ= shift T×2 π=0.25 2.0×2 π=π 4 or 45°.

6 a iZero

ii0.20 m

b x=0.20 sin(2 π 1.5 t+π 2)=0.20 sin(4 π 3 t+π 2)=0.20 cos(4 π 3 t).

7Comparing with x = x 0 sin(ω t) we find ω=π 3 and T=2 π ω=2 π π 3=6.0 s.

8 v max=ω x 0 and a max=ω 2 x 0 so a max v max=ω 2 x 0 ω x 0=ω=2 π T. So T=2 π v max a max=2 π×4.0 8.0=3.1 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.