Given any theoretical scenario, will a driven oscillator oscillate at ω0 (the natural spring frequency) after a long time? Why or why not?
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Given any theoretical scenario, will a driven oscillator oscillate at ω0 (the natural spring frequency) after a long time? Why or why not?
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- A coin is placed on a platform attached to a spring that oscillates vertically in simple harmonic motion. The amplitude of the displacement is 4.6cm. What is the maximum frequency for which the coin will always remain in contact with the platform?A car with a total mass of 1700 kgkg (including passengers) is driving down a washboard road with bumps spaced 4.1 mm apart. The ride is roughest—that is, the car bounces up and down with the maximum amplitude—when the car is traveling at 6.4 m/s. What is the spring constant of the car’s springs?A mass-spring-dashpot system is modeled by the differential equation: x" + 4x + 5x = f(t) (a) What is the type of oscillatory motion of the mass? Explain. (b) Find the transient solution of the system. (c) Find the steady state solution of the system for f(t) = 4 cos wt for w= 1. Write your solution as C cos (wt -a). (d) Solve the initial value problem for z(0) = 12, x'(0) = 0. (e) Draw the steady state solution and describe the oscillation.
- Calculate the velocity of a simple harmonic oscillator with amplitude of 19.9 cm and frequency of 5 Hz at a point located 5 cm away from the equilibrium position. Give your answer in SI units.A simple harmonic oscillator consists of a mass m attached to a spring with spring constant k, with displacement given by x = A sin(wt + ¢) . Which one of the following is NOT true? O The frequency is independent of the amplitude O The potential energy is a maximum when (wt + 4) = 0 The kinetic energy is a maximum when (wt + ¢) = 0 O The restoring force must be proportional to the negative of the displacement O Increasing the mass will decrease the frequencyAn oscillator is comprised of a 2.0-kg block and a 1200 N/m spring. The block is held at rest 2.5 cm from the equilibrium point and released. Assuming no friction, what is the block's maximum speed? 22 cm/s 61 cm/s 1.8 m/s 40 cm/s 87 cm/s