13. A particle is released from rest at a distance 4m from the origin and moves in simple harmonic motion according to the equation x" = -10°x (a) What is the period of the motion? 2 (b) What is the maximum speed of the particle? 2
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- 14. A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at and moves to the right. The amplitude of its motion is 2.00 cm, and the frequency is 1.50 Hz. (a) Write equation of harmonic oscillation x(t). Determine (b) the maximum speed and maximum acceleration of the particle. (c) Find the total distance traveled the particle between t=0 and t=10 s.1.A hoop is hung on a horizontal nail and undergoes small oscillations, once every 2 seconds. What is the radius of the hoop?1. A particle executes simple harmonic motion with an amplitude of 10 cm and time period 6 s. At t = 0 it is at position x= 5 cm going towards positive x-direction. Write the equation for the displacement x at time t. Find the magnitude of the acceleration of the particle at t = 4 s.
- A9- The period of a simple pendulum with length L is T=√L/g c) T = 2√g/L d) T=2m √ L/g A10- A particle is in simple harmonic motion with amplitude A. Its kinetic energy is a a) T=√g/L b) maximum at: c) x=1A/√2 d) x=1A a) x = 0 b)x=1A/25. Review. A particle moves along the x axis. It is initially at the position 0.270 m, moving with velocity 0.140 m/s and acceleration -0.320 m/s². Suppose it moves as a particle under constant acceleration for 4.50 s. Find (a) its position and Answer -2.34 m (b) its velocity at the end of this time interval. Next, assume it moves as a particle in simple harmonic motion for 4.50 s and x = 0 is its equilibrium position. Find Answer -1.30 m/s (c) its position and Answer -0.076 3 m (d) its velocity at the end of this time interval. Answer 0.315 m/s40. A particle is executing simple harmonic motion with amplitude 2 meters and period 12 seconds. What is the maximum speed in m/s of the particle? 6 3 36 D 3
- 4:29 M The equation of motion of a particle in simple harmonic motion is given by: x(t) = 0.2cos(wt), where x is in meters and t is in seconds. At x = 0, the particle's velocity is v = -1.256 m/s. The period of oscillation, T, equals: 1.5 sec 3 sec 0.25 sec 1 sec 0.5 sec Consider a place where the gravity is 4 times the gravity on Earth (g' = 4g), then the frequency of oscillation of a simple pendulum in that place, f', as compared to its frequency on earth is: f' = f/2 f' = 2f f' = 9f f' = f/3 f' = 4f II O O3. A mass on a spring moving along the x-axis in simple harmonic motion starts from the equilibrium position, the origin, at t = 0 and moves to the right (consider the right to be the positive x direction). The amplitude of its motion is 3.00 cm and the frequency is 1.50 Hz. At what earliest time does this mass have the maximum positive acceleration (i.e.pointing in the positive x direction)? X = 0 +x a. t= 0.500 seconds. b. t= 0.667 seconds. Ax с. t = = 1.50 seconds. d. t= 0.167 seconds. e. t= 0.314 seconds.1. A grandfather clock is constructed so that it has a simple pendulum that swings from one side to the other, a distance of 30.1 mm, in 1.00 s. what is the maximum speed of the pendulum bob?