16.2 Period and Frequency in Oscillations Figure 16.8 The strings on this guitar vibrate at regular time intervals. (credit JAR)
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Period and Frequency in Oscillations
• Observe the vibrations of a guitar string.
• Determine the frequency of oscillations.
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- 1. ••• A 1.80-kg block slides on a rough horizontal surface. Theblock hits a spring with a speed of 2.00 m/s and compresses ita distance of 11.0 cm before coming to rest. If the coefficient ofkinetic friction between the block and the surface is uk =0.560 ,what is the force constant of the spring? Draw and Explain.• Part A The two pendulums shown in the figure (Figure 1) each consist of a uniform solid ball of mass M supported by a massless string, but the ball for pendulum A is very tiny while the ball for pendulum B is much larger. You may want to review (Page). Find the period of pendulum A for small displacements. Express your answer in terms of the variables M, L. and appropriate constants. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Physical pendulum versus simple pendulum. Templates Symbols undo redo Teset keyboard shortouts Help T = Submit Requeet Answer • Part B Find the period of pendulum B for small displacements. Express your answer in terms of the variables M. L. and appropriate constants. Templates Symbols undo redo feset keyboard shortcuts help Tg = Submit Request Answer Part C Complete previous part(s) Provide Feedback Figure L/2 P Pearson Copyright © 2022 Pearson Educatlon Inc. All rights reserved.| Terms of Use | Privacy…PRACTICE IT Use the worked example above to help you solve this problem. (a) Find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is the following. A = f = T = a max (b) Find the maximum magnitude of the velocity and acceleration. Vmax x = V = = a = x = (0.245 m) cos(t) 8.00 = m Hz S (c) What are the position, velocity, and acceleration of the object after 1.50 s has elapsed? m m/s m/s² m/s m/s²
- 2 Exploring Harmonic Motion The following exercises will let you visualize the effects of modifying the parameters of a general sinusoidal function: f(t) = A · cos (wt + ¢) For each exercise, plot the two functions over the range 0 < t < 47 using your favorite graphing software. • You must submit all 5 plots for full credit. • Only extremely precise and accurate hand-drawn plots will receive full credit. For each part (a)-(e), describe the major differences between the two plotted functions. (a) fj(t) = cos t f2(t) = 2 cos t (b) f1(t) = cos t S2(1) = cos 2t (c) fi(t) = cost S2() = cos (1 + ) (d) f¡(t) = cost f2(t) = cos t + 2 cos (t + -) (e) fi(t) = cos t f2(t) = cos t + 2 cos 2tThe amplitude of an oscillator decreases to 36.7% of its initial value in 26.5 s. Part A What is the value of the time constant? Express your answer with the appropriate units. • View Available Hint(s) IH HẢ T = Value Units SubmitDamped Oscillations x(t) = xe cos(@'t+4) k @'= 2 m 4m? m • How does damping affect frequency? (A) No change (B) Increases frequency slightly (C) Decreases frequency slightly (D) Can either increase or decrease freq. slightly (E) Can't tellI
- In a simplified manner how do i find the amplitude and period of a spring oscillatorPart C A 210 g mass attached to a horizontal spring oscillates at a frequency of 5.50 Hz. At t = 0 s, the mass is at a = 4.40 cm and has vz = -44.0 cm/s. Determine the amplitude. %3D %3D Express your answer with the appropriate units. • View Available Hint(s) HA 國? A = Value Units Submit Part D Determine the phase constant. Express your answer with the appropriate units. • View Available Hint(s) НА фо Value UnitsA 500 g block connected to a light spring of which the force constant is 20 N/m oscillates on a horizontal, frictionless air surface. • Calculate the total energy of the system and the maximum speed of the block if the amplitude of the motion is 3 cm. • Compute the potential and kinetic energies of the system when the position is 2 Cm. • What is the velocity of the block when the position is 2 cm