For a spring: Initial values: initial displacement, x0 = 3 m initial velocity, v0 = 0...
For a spring:
Initial values:
initial displacement, x0 = 3 m
initial velocity, v0 = 0 m/s
mass, m = 100 kg
spring constant, k = 100 kg/s^2
Damping Force, Fr = a*v
where a is the damping factor
At t = 20 s, the amplitude of the oscillation is decreased to 1/2 of the initial
Find the frequency, v1 and the damping factor, a
Homework Answers
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For a spring:
Initial values:
initial displacement, x0 = 3 m
initial velocity, v0 = 0...
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped...
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped when moving in the vertical direction by a damping force Famp =-rý, where y is the 1200 kg sitting 4. (a) damping constant. If y is 90% of the critical value; what is the period of vertical oscillation of the car? () by what factor does the oscillation amplitude decrease within one period?...
A mass m = 3 kg is attached to a spring with spring constant k =...
A mass m = 3 kg is attached to a spring with spring constant k = 3 N/m and oscillates with simple harmonic motion along the x-axis with an amplitude A = 0.10 m. (a) What is the angular frequency of this oscillation? (b) What is the period T and the frequency f of the oscillation? (c) If the phase constant = 0, write down expressions for the displacement, velocity and acceleration of the mass as a function...
A 5 kg mass is hung on a spring with a stiffness of 70 N/m. find...
A 5 kg mass is hung on a spring with a stiffness of 70 N/m. find the oscillation response of this mass as a function of time, if x0 = 1 m and v0 = -0.45 m/s. x0 is the initial displacement and v0 is the initial speed. please show all work
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two per...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
PROBLEMS 89 3-30. A system composed of a mass of S kg and an elastic member having a modulus of 4...
Please answer 3-34 and 3-35. Please provide all steps so I can
follow along.
PROBLEMS 89 3-30. A system composed of a mass of S kg and an elastic member having a modulus of 45 N/m is less than critically damped. When the mass is givén an initial displacement and released from rest, the overshoot (the displacement attained past the equilibrium position) is 25% Determine the dam ping factor and the damping constant. 3-31. A mass-spring system is critically damped....
Ignore damping forces. A mass of 4 kg is attached to a spring with constant k- 16 N/m, then the s...
Ignore damping forces. A mass of 4 kg is attached to a spring with constant k- 16 N/m, then the spring is stretched 1 m beyond its natural length and given an initial velocity of 1 m/sec back towards its equilibrium position. Find the circular frequency ω, period T, and amplitude A of the motion. (Assume the spring is stretched in the positive direction.) A 7 kg mass is attached to a spring with constant k 112 N m. Given...
A spring stretches 0.150 m when a 0.300 kg. mass is hung vertically from it. From...
A spring stretches 0.150 m when a 0.300 kg. mass is hung vertically from it. From this information you can determine the spring constant, k. Next, the spring is set up horizontally with the 0.300 kg. mass resting on a frictionless table. The block is pushed so that the spring is compressed 0.100 m from the equilibrium point, and released from rest. Determine: The spring constant k (in N/m)? The amplitude of the horizontal oscillation (in m)? The angular frequency,...
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is...
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is driven by an external force with frequency w and amplitude Fo. 2662 where, wo is the (a) Show that the maximum oscillation amplitude occurs when w = natural frequency of the system. where, wd is the (b) Show that the maximum oscillation amplitude at that frequency is A = frequency of the undriven, damped system.
2. Following problem 1, the same spring-mass is oscillating, but the friction is involved. The spring-mass starts oscillating at the top so that its displacement function is x Ae-yt cos(wt)...
2. Following problem 1, the same spring-mass is oscillating, but the friction is involved. The spring-mass starts oscillating at the top so that its displacement function is x Ae-yt cos(wt)t is observed that after 5 oscillation, the amplitude of oscillations has dropped to three-quarter (three-fourth) of its initial value. (a) 2 pts] Estimate the value ofy. Also, how long does it take the amplitude to drop to one-quarter of initial value? 0 Co [2 pts] Estimate the value of damping...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped when moving in the vertical direction by a damping force Famp =-rý, where y is the 1200 kg sitting 4. (a) damping constant. If y is 90% of the critical value; what is the period of vertical oscillation of the car? () by what factor does the oscillation amplitude decrease within one period?...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
Please answer 3-34 and 3-35. Please provide all steps so I can
follow along.
PROBLEMS 89 3-30. A system composed of a mass of S kg and an elastic member having a modulus of 45 N/m is less than critically damped. When the mass is givén an initial displacement and released from rest, the overshoot (the displacement attained past the equilibrium position) is 25% Determine the dam ping factor and the damping constant. 3-31. A mass-spring system is critically damped....
Ignore damping forces. A mass of 4 kg is attached to a spring with constant k- 16 N/m, then the spring is stretched 1 m beyond its natural length and given an initial velocity of 1 m/sec back towards its equilibrium position. Find the circular frequency ω, period T, and amplitude A of the motion. (Assume the spring is stretched in the positive direction.) A 7 kg mass is attached to a spring with constant k 112 N m. Given...
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is driven by an external force with frequency w and amplitude Fo. 2662 where, wo is the (a) Show that the maximum oscillation amplitude occurs when w = natural frequency of the system. where, wd is the (b) Show that the maximum oscillation amplitude at that frequency is A = frequency of the undriven, damped system.
2. Following problem 1, the same spring-mass is oscillating, but the friction is involved. The spring-mass starts oscillating at the top so that its displacement function is x Ae-yt cos(wt)t is observed that after 5 oscillation, the amplitude of oscillations has dropped to three-quarter (three-fourth) of its initial value. (a) 2 pts] Estimate the value ofy. Also, how long does it take the amplitude to drop to one-quarter of initial value? 0 Co [2 pts] Estimate the value of damping...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
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