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Show that the equation-of-motion (EOM) that models the car, where the position of the mass is...
Please help me code in MATLAB Consider a car of mass M that varies according to...
Please help me code in MATLAB Consider a car of mass M that varies according to y, D sin (ot). The car is equipped with springs and shock absorbers and the vertical motion of the car is described by the following equation: d2y y(0)0 where M is the mass of the car (3000 lbm), y is the vertical displacement of the car in inches, t is the time in seconds, k is the spring constant (700 lbf/in), D is the...
The motion of a pendulum bob with mass m is governed by the equation mL0" (t) + mg sin θ (t)-0 where L is the lengt...
The motion of a pendulum bob with mass m is governed by the equation mL0" (t) + mg sin θ (t)-0 where L is the length of the pendulum arm, g 3 and θ is the angle (in radians) between the pendulum arm and the vertical. Suppose L 16 ft and the bob is set in motion with (0 1 and 0' (0)--3. Find the second degree Taylor polynomial P2(t) that approximates the angular position θ(t) of the bob near...
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is...
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my'' (t) + by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 10 kg, b = 100 kg/sec, k = 260 kg/sec?. y(0) = 0.3 m, and y'(0) = -0.4 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point?...
Consider the step response of the motion of a car. Use the following parameters: mass =...
Consider the step response of the motion of a car. Use the following parameters: mass = 800kg, drag coefficient = 225Ns/m, step input amplitude = 15000N. Using MATLAB, create a graph to illustrate the step response of the car. Annotate the graph to show the time constant and the steady state speed.
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
Consider the spring-mass system described by the equation my''+By+ky=0, where y denotes the distance from equilibrium....
Consider the spring-mass system described by the equation my''+By+ky=0, where y denotes the distance from equilibrium. Suppose that mass is 3kg and that there is no friction. The spring is stretched by 0.1 m and then struck with a hammer so that y(0)=-0.1 and y'(0)=1, as a result, the mass begins to oscillate at the rate of 4 radians per second. a) What is the spring constant? Justify your answer by computing the homogeneous solution. b) What is the amplitude...
Consider the spring-mass system described by the equation my''+By+ky=0, where y denotes the distance from equilibrium. Suppose that mass is 3kg and that there is no friction. The spring is str...
Consider the spring-mass system described by the equation my''+By+ky=0, where y denotes the distance from equilibrium. Suppose that mass is 3kg and that there is no friction. The spring is stretched by 0.1 m and then struck with a hammer so that y(0)=-0.1 and y'(0)=1, as a result, the mass begins to oscillate at the rate of 4 radians per second. a) What is the spring constant? Justify your answer by computing the homogeneous solution. b) What is the amplitude...
What is the general solution for overdamped motion equation? Show that the mass can pass through...
What is the general solution for overdamped motion equation? Show that the mass can pass through the equilibrium position at most once, regardless of the initial conditions Free-body diagram System (b) (a) Rajah 4/Figure 4 (15 markah/marks)
A mass is attached to a spring & is oscillating up & down. The position of...
A mass is attached to a spring & is oscillating up & down. The position of the oscillating mass is given by... y=(3.2 cm)*Cos[2*3.14*t/(0.58 sec)]; where t is time. Determine (a) the period of this motion; (b) the first time the mass is at position y=0. Please show all work.
The differential equation describing the motion of a mass attached to a spring is x'' +...
The differential equation describing the motion of a mass attached to a spring is x'' + 16x = 0. If the mass is released at t = 0 from 1 meter above the equilibrium position with a downward velocity of 3 m/s, the amplitude of vibrations is Please show all work. Thank you!
Please help me code in MATLAB Consider a car of mass M that varies according to y, D sin (ot). The car is equipped with springs and shock absorbers and the vertical motion of the car is described by the following equation: d2y y(0)0 where M is the mass of the car (3000 lbm), y is the vertical displacement of the car in inches, t is the time in seconds, k is the spring constant (700 lbf/in), D is the...
The motion of a pendulum bob with mass m is governed by the equation mL0" (t) + mg sin θ (t)-0 where L is the length of the pendulum arm, g 3 and θ is the angle (in radians) between the pendulum arm and the vertical. Suppose L 16 ft and the bob is set in motion with (0 1 and 0' (0)--3. Find the second degree Taylor polynomial P2(t) that approximates the angular position θ(t) of the bob near...
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my'' (t) + by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 10 kg, b = 100 kg/sec, k = 260 kg/sec?. y(0) = 0.3 m, and y'(0) = -0.4 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point?...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
What is the general solution for overdamped motion equation? Show that the mass can pass through the equilibrium position at most once, regardless of the initial conditions Free-body diagram System (b) (a) Rajah 4/Figure 4 (15 markah/marks)
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