1. Characterizing Oscillations (a) An object is moving with uniform circular motion, making 104 revolutions in a time of 40 ms. (i) What is the period? (ii) What is the frequency? (iii) What is the angular frequency? 1.5 1.0 (b) Write the equation of motion for the graph: 0.5 0.0 -0,5 -1.0 -1.5 12 4 6. 10 14 16 18 t [seconds] y [meters]
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A: This question is from oscillation and based on graph.
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- 5. A child on a swing set swings back and forth with a period of 3.3 s and an amplitude of 25 degrees. What is the maximum speed of the child as she swings?1. A pendulum with mass 2kg, length 2.5m swings with amplitude A = 2cm. After a long time the amplitude decreases to 1 cm due to air drag. How long is the period after the amplitude decrease? 2. What is the period of oscillation of the pendulum before and after the amplitude change?2. The motion of a pendulum is described by 0(t) = 0 cos() where L = 1.5 m and mass m=1.0 kg. (a) Find e (radian) from the figure and calculate the period T. (b) Plot 0(1), w(t) x(t), and dt d? a(t): e(t) for t=0 – 2.0T in the following graph. dr Pivot point 50 Omax = 1/2T 1T 3/2T 2T 2.5T w(t) = a(t) =
- A pendulum has a period of 1.35 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth? (Assume: The length is to be the same for the pendulum both on Mars and on Earth) 9. [Ans: 2.2 s]5. Two pendulums of lengths L₁ and L2 and when located at the respective distances R₁ and R₂ from the center of the earth -have periods p₁ and P2. Show that P₁_R₁L₁ R₂√L₂ P2 = Assume that the differential equation of a simple pendulum of length L is LO"+ge = 0, where g = GM/R2 is the gravitational acceleration at the location of the pendulum (at distance R from the center of the earth; M denotes the mass of the earth).A given mass and spring system oscillates with an amplitude A and a period T. When the amplitude is doubled, when then happens to the period? Be specific 4x, 2x, the same, ½ x, ¼ x, etc Explain
- Based on Graphs 3 and 4, is the radius directly or inversely proportional to the square of the period? Explain your reasoning.10. A block hangs on a spring attached to the ceiling and is pulled down 6 inches below itsequilibrium position. After release, the block makes one complete up-and-down cycle in 2seconds and follows simple harmonic motion. a. What is the period of the motion? b. What is the frequency? c. What is the amplitude? d. Write a function to model the displacement ? (in inches) as a function of the time ? (in seconds) after release. Assume that a displacement above the equilibrium point is positive.e. Find the displacement of the block and direction of movement at ? = 1 sec.3) an air track glider attached to a spring oscillates AP between the 8.00cm mark and the 57.0cm mark A On Din 29.0S, the track. The glider completes 8.00 oscillations Please include units! What is the period of oscillations? What is the frequency of oscillations? What is the angular frequency of oscillations? What is the amplitude? What is the maximum speed of the glide A no alero no ider? m bao da to
- A 3.7 kg mass attached to an ideal spring oscillates horizontally with an amplitude of 2.01 m. The spring constant is 137.29 N/m. What is the period of the motion? Round off your final answer to two decimal places. Add your answer23) A simple pendulum of length 2.58 m is used to measure the acceleration of gravity at the surface of a distant planet. If the period of such a pendulum is 9.18 seconds, what is the acceleration of gravity? A) 23.7 m/s2 B) 1.21 m/s2 c) 1.77 m/s2 d) 0.83 m/s2 e) 2.42 m/s24