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Phys101 Term:121 Online HW-Ch15-Lec02 Q1: A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only when the displacement is: A. zero B. ±A/2 C. ±A√2/2 D. ±A/4 E. anywhere between -A and +A Ans: 𝐂; K = U and ω2 = ⇒ 1 1 mv 2 = kx 2 ⇒ m �ω2 A2 sin2 (ωt) = k�A2 cos2 (ωt)�� 2 2 k ⇒ k = mω2 ; so sin2 (ωt) = cos2 (ωt) m tan2 (ωt) = 1 → tan(ωt) = ±1 ⇒ ωt = ± ∴ x = A cos( ωt) = ±A Q2: √2 2 π 4 Three physical pendulums of masses m 1 = m o , m 2 = 2m o , m 3 =3m o have the same shape, size and are suspended at the same point. Rank the masses according to the period of the pendulums, least first. A. B. C. D. E. 1, then 2, then 3. 2, then 3, then 1. 3, then 1, then 2. 3, then 2, then 1. All have the same period Ans: E, the mas will cancel out in the equation of the period of a physical pendulum KFUPM-Physics Department 1 Phys101 Term:121 Online HW-Ch15-Lec02 Q3: A meter stick is pivoted at one of its edges and is free to oscillate in a vertical plane on a planet of unknown gravitational acceleration g. The meter stick is moved from the equilibrium position by an angle of 15o and then released. Find the gravitational acceleration (in m/s2) of the planet if the period of oscillation is measured to be 2 s. (Give your answer in three significant figures form) Ans: 1 2 ML ; L = 1 meter 3 L h = = 0.5 2 I= T = 10 s; I 4π2 × I 4π2 × ML2 /3 T = 2π� ⇒g= 2 = Mgh T Mh T 2 Mh ⇒g= 4π2 × 1/3 = 6.58 m/s2 22 × 0.5 KFUPM-Physics Department 2