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# 341h5 - M341 H5(S Zhang 3.4 1 EP 3.4 1 3 5 14 15 18 32 33...

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M341 H5 (S. Zhang) 3.4. 1. EP § 3.4: 1, 3, 5, 14, 15, 18, 32, 33 ans: 2. Determine the period and frequency of the simple har- monic motion of a 4-kg mass on the end of a pring with spring constant 16N/m. ans: ( ) EP § 3.4: 1 Freqency ω 0 = k m = 48 0 . 75 = 8 rad sec = 4 π Hz Period T = 2 π ω 0 = π 4 sec 3. A mass of 3kg is attached the end of a pring that is stretched 20 cm by a force of 15 N. It is set in motion with initial position x 0 = 0 and initial velocity v 0 = - 10m/s. Find the amplitude, period, and frequency of the resulting motion. ans: ( ) EP § 3.4: 3 The spring constant k = 15 / 0 . 2 = 75 N/m The solution for 3 x + 75 x = 0 , x (0) = 0 , x (0) = - 10 is x ( t ) = - 2 sin 5 t The amlitude is 2 m; the frequency is ω 0 = k m = 5 rad/sec = 2 . 5 π Hz The period is T = 2 π 5 sec 4. Assume that the equation for a simple pendulum of length L is + = 0 where g = GM/R 2 . Two pendulums are of lengths L 1 and L 2 and – when located at the respetive distances R 1 and R 2 from the center of the earth – having periods p 1 and p 2 . Show that p 1 p 2 = R 1 L 1 R 2 L 2 ans: ( ) EP § 3.4: 5 When θ small, the equation for a pendulum is θ + g L θ = 0 g = GM/R 2 The circular frequency ω

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341h5 - M341 H5(S Zhang 3.4 1 EP 3.4 1 3 5 14 15 18 32 33...

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