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1. A force F(t) is suddenly applied to a mass m, which is supported by a...
1. A mass m, initially at rest, is subject to a constant applied force F. After the mass has trav...
1. A mass m, initially at rest, is subject to a constant applied force F. After the mass has travelled a distance xo it impacts a damper with damping coeficient b. Assume the surface is frictionless Xo a. Formulate the first order differential equation describing the velocity of the car as a function of time, before the collision. What is the velocity at the collision? b. Formulate the first order differential equation describing the system after the collision. C. What...
6) The 18 kg mass of a spring-mass system is initially at rest. At time =...
6) The 18 kg mass of a spring-mass system is initially at rest. At time = 0, a 400 N force is applied (toward the right). Spring constant is 100 kN / m, and the viscous damping coefficient is 520 Ns/m Determine the transient response F = (400 N) 1(t) Delay time [HINT: may need to a) graphing calculator, fixed point iteration; or calculator equation solver] b) c) use a m Peak time Maximum overshoot (in mm)
6) The 18...
The same constant force, F, is applied to two blocks. The first block has a mass...
The same constant force, F, is applied to two blocks. The first
block has a mass of M and the second block has a mass of 2M. Both
blocks are initially at rest and the force acts on each of them for
the same period of time, t.
15) After time, t, which block has
more momentum?
a)The block of mass M
b)The block of mass 2M
c)They will have the same momentum
16) After time, t, which block has
more kinetic...
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use...
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use a free-body diagram and apply Newton's 2nd Law to show that the upward displacement of the mass, r(t), can be modelled with the ODE da da mdt2 + cat + kz = F(t) where k is the spring coefficient and c is the damping coefficient. = 2 kg, c = For the remainder of the questions, use the following values: m 8 Ns/m, k...
Question 5: Prove the following: a) Theorem 5.1: If then Page 3 of 8 te, 2017 SEE307 Systems and Signals Trimester 1, 2017 1Uw).su»-1 {Lh(thu-thar} = F(s)Kfs) where L(.) represents the Laplace t...
Question 5: Prove the following: a) Theorem 5.1: If then Page 3 of 8 te, 2017 SEE307 Systems and Signals Trimester 1, 2017 1Uw).su»-1 {Lh(thu-thar} = F(s)Kfs) where L(.) represents the Laplace transform. (15 marks) b) The output ) of an analog averager is given by which corresponds to the accumulation of values of x() in a segment [t-T.r]divided by its length T, or the average of x(0) in [t-T,1]. Use the convolution integral to find the response of the...
14. A bucket of mass m is being drawn up a well by a rope which exerts a steady force F. Initially the bucket conta...
14. A bucket of mass m is being drawn up a well by a rope which exerts a steady force F. Initially the bucket contains a mass mo of water, but this leaks out at a constant rate so that after time t the bucket is empty, before it reaches the top of the well. What is the velocity of the bucket when it is just empty?
14. A bucket of mass m is being drawn up a well by...
winkngs spring i(t) v(t) st VEE Figure 1: (a)Solenoid with retu spring. (b) Equivalent lumped electrical cireuit (...
winkngs spring i(t) v(t) st VEE Figure 1: (a)Solenoid with retu spring. (b) Equivalent lumped electrical cireuit (e) Equivalent mechanical diagram Figure 1(a) illustrates a solenoid with a return spring The voltage e(t) across the winding, causes a current it) to flow through the winding. which in turn generates a magnetic field The magnetic field induces a force f(t) on the plunger mass, . The magnitude of this force is related to the current in the windings via the solenoid's...
An object of mass m is initially at rest. After a force of magnitude F acts...
An object of mass m is initially at rest. After a force of magnitude F acts on it for a time T, the object has a speed v. Suppose the mass of the object is doubled, and the magnitude of the force acting on it is quadrupled. In terms of T, how long does it take for the object to accelerate from rest to a speed v now? T′/T T′/T =
A damped forced oscillation with mass-spring sys- tem is modeled as an nonhomogeneous ODE as following:...
A damped forced oscillation with mass-spring sys- tem is modeled as an nonhomogeneous ODE as following: my" + cy' + ky = r(t) where m = 1 kg, k = 1 N/m and c = 2 N m/s. Initially, y(0) 1m y(0) = -1m/s. r(t) is the input force for this system. Initially (t = (s), there is no input force for this system r(t) = 0 N. At time t = 2s, a costant force (r(t) = 2 N)...
USE DEFINITION 1 TO DETERMINE THE LAPLACE TRANSFORM OF THE FOLLOWING FUNCTION. f(t)= e sin(t) Laplace...
USE DEFINITION 1 TO DETERMINE THE LAPLACE TRANSFORM OF THE FOLLOWING FUNCTION. f(t)= e sin(t) Laplace Transform Definition 1. Let f(t)be a function on [0,00). The Laplace transform of f is the function defined by the integral The domain of F(s) is all the values of " for which the integral in (1) exists.' The Laplace transform of fis denoted by both and ${/}. QUESTION 2. (3PTS) USE TABLE 7.1 AND 7.2 TO DETERMINE THE LAPLACE TRANSFORM OF THE GIVEN...
1. A mass m, initially at rest, is subject to a constant applied force F. After the mass has travelled a distance xo it impacts a damper with damping coeficient b. Assume the surface is frictionless Xo a. Formulate the first order differential equation describing the velocity of the car as a function of time, before the collision. What is the velocity at the collision? b. Formulate the first order differential equation describing the system after the collision. C. What...
6) The 18 kg mass of a spring-mass system is initially at rest. At time = 0, a 400 N force is applied (toward the right). Spring constant is 100 kN / m, and the viscous damping coefficient is 520 Ns/m Determine the transient response F = (400 N) 1(t) Delay time [HINT: may need to a) graphing calculator, fixed point iteration; or calculator equation solver] b) c) use a m Peak time Maximum overshoot (in mm)
6) The 18...
The same constant force, F, is applied to two blocks. The first
block has a mass of M and the second block has a mass of 2M. Both
blocks are initially at rest and the force acts on each of them for
the same period of time, t.
15) After time, t, which block has
more momentum?
a)The block of mass M
b)The block of mass 2M
c)They will have the same momentum
16) After time, t, which block has
more kinetic...
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use a free-body diagram and apply Newton's 2nd Law to show that the upward displacement of the mass, r(t), can be modelled with the ODE da da mdt2 + cat + kz = F(t) where k is the spring coefficient and c is the damping coefficient. = 2 kg, c = For the remainder of the questions, use the following values: m 8 Ns/m, k...
Question 5: Prove the following: a) Theorem 5.1: If then Page 3 of 8 te, 2017 SEE307 Systems and Signals Trimester 1, 2017 1Uw).su»-1 {Lh(thu-thar} = F(s)Kfs) where L(.) represents the Laplace transform. (15 marks) b) The output ) of an analog averager is given by which corresponds to the accumulation of values of x() in a segment [t-T.r]divided by its length T, or the average of x(0) in [t-T,1]. Use the convolution integral to find the response of the...
14. A bucket of mass m is being drawn up a well by a rope which exerts a steady force F. Initially the bucket contains a mass mo of water, but this leaks out at a constant rate so that after time t the bucket is empty, before it reaches the top of the well. What is the velocity of the bucket when it is just empty?
14. A bucket of mass m is being drawn up a well by...
winkngs spring i(t) v(t) st VEE Figure 1: (a)Solenoid with retu spring. (b) Equivalent lumped electrical cireuit (e) Equivalent mechanical diagram Figure 1(a) illustrates a solenoid with a return spring The voltage e(t) across the winding, causes a current it) to flow through the winding. which in turn generates a magnetic field The magnetic field induces a force f(t) on the plunger mass, . The magnitude of this force is related to the current in the windings via the solenoid's...
A damped forced oscillation with mass-spring sys- tem is modeled as an nonhomogeneous ODE as following: my" + cy' + ky = r(t) where m = 1 kg, k = 1 N/m and c = 2 N m/s. Initially, y(0) 1m y(0) = -1m/s. r(t) is the input force for this system. Initially (t = (s), there is no input force for this system r(t) = 0 N. At time t = 2s, a costant force (r(t) = 2 N)...
USE DEFINITION 1 TO DETERMINE THE LAPLACE TRANSFORM OF THE FOLLOWING FUNCTION. f(t)= e sin(t) Laplace Transform Definition 1. Let f(t)be a function on [0,00). The Laplace transform of f is the function defined by the integral The domain of F(s) is all the values of " for which the integral in (1) exists.' The Laplace transform of fis denoted by both and ${/}. QUESTION 2. (3PTS) USE TABLE 7.1 AND 7.2 TO DETERMINE THE LAPLACE TRANSFORM OF THE GIVEN...
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