Consider a small mass performing simple harmonic motion with angular frequency 10 rad/s. If we know that at t = 0 the mass is at ro = +5 cm moving to the right at +87 cm/s, and we want to represent the oscillations using a cos function then . (a) Find the amplitude of the oscillations (b) Find the phase constant of the oscillations (c) Find the maximum speed of the mass (d) Find the maximum acceleration of the mass

Consider a small mass performing simple harmonic motion with angular frequency 10 rad/s. If we know that at t = 0 the mass is at ro = +5 cm moving to the right at +87 cm/s, and we want to represent the oscillations using a cos function then . (a) Find the amplitude of the oscillations (b) Find the phase constant of the oscillations (c) Find the maximum speed of the mass (d) Find the maximum acceleration of the mass

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter12: Coupled Oscillations

Section: Chapter Questions

Problem 12.3P

See similar textbooks

Similar questions

Show that, if a driven oscillator is only lightly damped and driven near resonance, the Q of the system is approximately Q2(TotalenergyEnergylossduringoneperiod)
Check Your Understanding Why are completely undamped harmonic oscillators so rare?
A mass m0is attached to a spring and hung vertically. The mass is raised a short distance in the vertical direction and released. The mass oscillates with a frequency f0. If the mass is replaced with a mass nine times as large, and the experiment was repeated, what would be the frequency of the oscillations in terms of f0?
Prove that using x(t)=Asin(t+) will produce the same results for the period for the oscillations of a mass and a spring. Why do you think the cosine function was chosen?
Plot a velocity resonance curve for a driven, damped oscillator with Q = 6, and show that the full width of the curve between the points corresponding to is approximately equal to ω0/6.
Let the initial position and speed of an overdamped, nondriven oscillator be x0 and v0, respectively. (a) Show that the values of the amplitudes A1 and A2 in Equation 3.44 have the values A1=2x0+v021 and A2=1x0+v021 where 1 = 2 and 2 = + 2. (b) Show that when A1 = 0, the phase paths of Figure 3-11 must be along the dashed curve given by x=2x, otherwise the asymptotic paths are along the other dashed curve given by x=1x. Hint: Note that 2 1 and find the asymptotic paths when t .
Find the frequency of a tuning fork that takes 2.50103 s to complete one oscillation.
Obtain the response of a linear oscillator to a step function and to an impulse function (in the limit τ → 0) for overdamping. Sketch the response functions.
Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.
Consider a simple harmonic oscillator consisting of a one kilogram mass m' on a spring with spring/forceconstant k and length L'. If the mass of the spring ms is 9% of the attached mass, and k = 66 N/m,and if we determined the attached body is displaced 3 cm and given a downward velocity of 0.4 m/s -calculate,→ the frequency ω of the motion, ,→ and the amplitude A of the motion
Prove that using x(t) = Asin (ωt + ϕ) will produce the same results for the period for the oscillations of a mass and a spring. Why do you think the cosine function was chosen?
The equation of motion for a damped harmonic oscillator is s(t) = Ae^(−kt) sin(ωt + δ),where A, k, ω, δ are constants. (This represents, for example, the position of springrelative to its rest position if it is restricted from freely oscillating as it normally would).(a) Find the velocity of the oscillator at any time t.(b) At what time(s) is the oscillator stopped?