A 0.420-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.8 cm. (Assume the position of the object is at the origin at t=0.)(a) Calculate the maximum value of its speed.288.64×Have you calculated the angular velocity? You almost always need this quantity for problems involving simple harmonic motion. cm/s(b) Calculate the maximum value of its acceleration.7714.29Write down the equation for x(t) and then think about how to find the acceleration as a function of time from this equation. cm/s²(c) Calculate the value of its speed when the object is 8.80 cm from the equilibrium position.167.33Can you determine a time when the object is at this position? You can then use this time in your equation of motion. cm/s(d) Calculate the value of its acceleration when the object is 8.80 cm from the equilibrium position.6285.71×How can you determine the force that acts on the object at this position? cm/s²(e) Calculate the time interval required for the object to move from x = 0 to x = 4.80 cm.0.042xCan you use your equation for x(t) to determine the time for the object to first reach 4.80 cm? s

an ideal gas undergoing an isothermal and reversible compression in a piston-cylinder device, here's…

Answered: A 0.420-kg object attached to a spring…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 29P: The angular position of a pendulum is represented by the equation = 0.032 0 cos t, where is in...

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For each expression, identify the angular frequency , period T, initial phase and amplitude ymax of the oscillation. All values are in SI units. a. y(t) = 0.75 cos (14.5t) b. vy (t) = 0.75 sin (14.5t + /2) c. ay (t) = 14.5 cos (0.75t + /2) 16.3
We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
A grandfather clock has a pendulum length of 0.7 m and mass bob of 0.4 kg. A mass of 2 kg falls 0.8 m in seven days to keep the amplitude (from equilibrium) of the pendulum oscillation steady at 0.03 rad. What is the Q of the system?
A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where U0 and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
The expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time, with x in centimeters and t in seconds. What are the a. frequency, b. period, c. amplitude, and d. initial phase of the objects motion? e. What is the position of the particle at t = 1.45 s?
The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?
A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates with an amplitude of 4.00 cm on a frictionless, horizontal surface. Find (a) the total energy of the system and (b) the speed of the object when its position is 1.00 cm. Find (c) the kinetic energy and (d) the potential energy when its position is 3.00 cm.
Consider the simplified single-piston engine in Figure CQ15.13. Assuming the wheel rotates with constant angular speed, explain why the piston rod oscillates in simple harmonic motion.
A simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.
A nylon siring has mass 5.50 g and length L = 86.0 cm. The lower end is tied to the floor, and the upper end is tied to a small set of wheels through a slot in a track on which the wheels move (Fig. P18.76). The wheels have a mass that is negligible compared with that of the siring, and they roll without friction on the track so that the upper end of the string is essentially free. Figure P18.76 At equilibrium, the string is vertical and motionless. When it is carrying a small-amplilude wave, you may assume the string is always under uniform tension 1.30 N. (a) Find the speed of transverse waves on the siring, (b) The string's vibration possibilities are a set of standing-wave states, each with a node at the fixed bottom end and an antinode at the free top end. Find the node-antinode distances for each of the three simplest states, (c) Find the frequency of each of these states.
Consider the simplified single-piston engine in Figure CQ12.13. Assuming the wheel rotates with constant angular speed, explain why the piston rod oscillates in simple harmonic motion. Figure CQ12.13

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