Homework Answers
(1 point) A mass of M 4 on a spring with k 7 and a damping...
(1 point) A mass of M 4 on a spring with k 7 and a damping constant D 3. Suppose that Fo- 4 Using forcing function Focos(ut) , find the w that causes the forced response with largest amplitude.
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness...
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness k-1000N/m, and damping c-200Ns/m. 1) Suppose that the mass is initially at rest and is given an initial velocity of 3 m/s Find the free vibration response of the mass. 2) Suppose that at a later time, a harmonic force F (t)- sin15t is acted on the mass. Determine the amplitude of the forced vibration response. F, sin
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.
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...
1. The exponential damping factor K of a spring is 1/10 the critical value. The spring...
1. The exponential damping factor K of a spring is 1/10 the critical value. The spring has an undamped frequency of wo. A mass m is attached to the spring. Find a) The resonant frequency in terms of w. (3 marks) b) The quality factor (1 mark) c) The phase angle when the spring is driven by a force F. at a driving frequency (1 marks) d) The steady-state amplitude of oscillation when it is driven at this frequency in...
(1) Suppose that the mass in a mass-spring-dashpot system with m = 10, the damping constant...
(1) Suppose that the mass in a mass-spring-dashpot system with m = 10, the damping constant c = 9 and the spring constant k = 2 is set in motion with x(0) = −1/2 and x′(0) = −1/4. (a)[5 pts] Find the position function x(t). (b)[5 pts] Determine whether the mass passes through its equilibrium position. Sketch the graph of x(t).
1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is a...
Differntial Equations Forced Spring Motion
1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is attached to a machine that supplies an external driving force of f(t) = 4 cos(wt). The systern is started from equilibrium i.e. 2(0) = 0 and z'(0) = 0. There is no damping. (a) Find the position x(t) of the mass as a function of time (b) write your answer in the form r(t)-1 sin(6t)...
(1 point) A mass m = 4 kg is attached to both a spring with spring...
(1 point) A mass m = 4 kg is attached to both a spring with spring constant k = 325 N/m and a dash-pot with damping constant c=4N s/m. The mass is started in motion with initial position Xo = 1 m and initial velocity vo = 9 m/s. Determine the position function z(t) in meters. x(t) = Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form x(t)...
(By hand) Suppose a spring-mass-damper system with mass m, linear damping coefficient cand spring constant k...
(By hand) Suppose a spring-mass-damper system with mass m, linear damping coefficient cand spring constant k is subject to a force given by Equation 1 above. Determine the steady state response of the system to the above force. f(t) = 3 1-1 - 7/2 <t<o 1 0<t</2 1
A spring is suspended vertically from a fixed support. The spring has spring constant k=24 N m −1 k=24 N m−1 . An object...
A spring is suspended vertically from a fixed support. The
spring has spring constant k=24 N m −1 k=24 N m−1 . An object of
mass m= 1 4 kg m=14 kg is attached to the bottom of the spring. The
subject is subject to damping with damping constant β N m −1 s β N
m−1 s . Let y(t) y(t) be the displacement in metres at the end of
the spring below its equilibrium position, at time t...
(1 point) A mass of M 4 on a spring with k 7 and a damping constant D 3. Suppose that Fo- 4 Using forcing function Focos(ut) , find the w that causes the forced response with largest amplitude.
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness k-1000N/m, and damping c-200Ns/m. 1) Suppose that the mass is initially at rest and is given an initial velocity of 3 m/s Find the free vibration response of the mass. 2) Suppose that at a later time, a harmonic force F (t)- sin15t is acted on the mass. Determine the amplitude of the forced vibration response. F, sin
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.
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...
1. The exponential damping factor K of a spring is 1/10 the critical value. The spring has an undamped frequency of wo. A mass m is attached to the spring. Find a) The resonant frequency in terms of w. (3 marks) b) The quality factor (1 mark) c) The phase angle when the spring is driven by a force F. at a driving frequency (1 marks) d) The steady-state amplitude of oscillation when it is driven at this frequency in...
Differntial Equations Forced Spring Motion
1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is attached to a machine that supplies an external driving force of f(t) = 4 cos(wt). The systern is started from equilibrium i.e. 2(0) = 0 and z'(0) = 0. There is no damping. (a) Find the position x(t) of the mass as a function of time (b) write your answer in the form r(t)-1 sin(6t)...
(1 point) A mass m = 4 kg is attached to both a spring with spring constant k = 325 N/m and a dash-pot with damping constant c=4N s/m. The mass is started in motion with initial position Xo = 1 m and initial velocity vo = 9 m/s. Determine the position function z(t) in meters. x(t) = Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form x(t)...
(By hand) Suppose a spring-mass-damper system with mass m, linear damping coefficient cand spring constant k is subject to a force given by Equation 1 above. Determine the steady state response of the system to the above force. f(t) = 3 1-1 - 7/2 <t<o 1 0<t</2 1
A spring is suspended vertically from a fixed support. The
spring has spring constant k=24 N m −1 k=24 N m−1 . An object of
mass m= 1 4 kg m=14 kg is attached to the bottom of the spring. The
subject is subject to damping with damping constant β N m −1 s β N
m−1 s . Let y(t) y(t) be the displacement in metres at the end of
the spring below its equilibrium position, at time t...
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