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Problem 2. (6 pts: 2 + 2 + 2) A car oscillates vertically on a bumpy...
A 2kg mass is suspended vertically from a spring attached to a fixed support. The spring...
A 2kg mass is suspended vertically from a spring attached to a fixed support. The spring satisfies Hooke's law with a spring constant of k 18 N m1. No damping is present. Gravity acts on the mass with a gravitational constant of g 10 m s2. An external force of R 24 sin (wt) Newton is applied to the mass, directed downwards, where t is the time in seconds since the mass was set in motion and w is a...
Consider a spring of mass 1 Kg attached to a spring obeying Hooke's Law with spring...
Consider a spring of mass 1 Kg attached to a spring obeying
Hooke's Law with spring constant K
Problem 4. (15 pts) Consider a spring of mass 1 kg attached to a spring obeying Hooke's Law with spring constant k N/m. Suppose an external force F(t) = 2 cos 3t is applied to the mass, and suppose the spring experiences no damping. Suppose the spring can be displaced 0.2 m by a 1.8 N force. If the spring is stretched...
x(t) y(d) Consider the spring-mass-damper system above travelling along a bumpy surface with a height change....
x(t) y(d) Consider the spring-mass-damper system above travelling along a bumpy surface with a height change. The damping ratio is =0.2, the natural frequency is 3 rad/s, and the mass, m=200 kg. The wheel does not lose contact with the road and the road has the shape, y(d)4sin 0H(d 10) where d is distance in meters, and y(d) is the height in centimeters 1. Write the ordinary differential equation for v-1 m/s and v-5 m/s. 2. The solution of x(t)...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
Amass of m 1.78 kg connected to a spring oscillates on a horizontal frictionless surface as...
Amass of m 1.78 kg connected to a spring oscillates on a horizontal frictionless surface as shown in the figure. The equation of motion of the mass is given by X = 0.303 cos(2.460) where the position x is measured in meters, the time t in seconds. Determine the period of the motion, * Tries 0/12 What is the maximum speed reached by the mass? * Tries 0/12 Determine the spring constant. BON Tring /12
show steps please A2. A simplified car model is shown in Figure A3. It travels horizontally at a constant speed of v 20...
show steps please
A2. A simplified car model is shown in Figure A3. It travels horizontally at a constant speed of v 20 miles perhour on a bumpy road (1 mile is approximately 1610 meters). The road surface is assumed to be rigid and has a sinusoidal profile. Both masses vibrate only in the vertical direction. m 900kg, m 60kg,k 1,000,000N/m m1 0.5 m 4k 0.1 m Figure A2. [15] [10] (1) Derive the equation of motion for the vertical...
A 2.65 kg mass oscillates back and forth on a spring with a velocity vector that...
A 2.65 kg mass oscillates back and forth on a spring with a velocity vector that varies as a function of time according to the following v(t)=(3.95cm/s) sin [0.79 rad/s] What is the maximum speed of mass What is the spring constant if the spring in n:m How fast us the mass moving at t= 5.0 sec in m/s
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...
A 200 g mass attached to a horizontal spring oscillates according to v(t) = .07 sin...
A 200 g mass attached to a horizontal spring oscillates according to v(t) = .07 sin (500t) 1. what is the total energy of the system? 2. how fast is it moving at t=5s? 3. construct an equation for the position as a function of time. 4. construct an equation for the acceleration as a function of time.
. A mass is attached to a spring. The position of the mass as it oscillates...
. A mass is attached to a spring. The position of the mass as it oscillates on the spring is given by: y = A cos (8.2t) where the value of t is in seconds and A is 6.2 cm. (a) What is the period of the oscillator? (2 pts) (b) What is the velocity of the oscillator at time t = 0 and at time t = T/4? Give magnitude and direction (+ or – y direction). (4 pts)...
A 2kg mass is suspended vertically from a spring attached to a fixed support. The spring satisfies Hooke's law with a spring constant of k 18 N m1. No damping is present. Gravity acts on the mass with a gravitational constant of g 10 m s2. An external force of R 24 sin (wt) Newton is applied to the mass, directed downwards, where t is the time in seconds since the mass was set in motion and w is a...
Consider a spring of mass 1 Kg attached to a spring obeying
Hooke's Law with spring constant K
Problem 4. (15 pts) Consider a spring of mass 1 kg attached to a spring obeying Hooke's Law with spring constant k N/m. Suppose an external force F(t) = 2 cos 3t is applied to the mass, and suppose the spring experiences no damping. Suppose the spring can be displaced 0.2 m by a 1.8 N force. If the spring is stretched...
x(t) y(d) Consider the spring-mass-damper system above travelling along a bumpy surface with a height change. The damping ratio is =0.2, the natural frequency is 3 rad/s, and the mass, m=200 kg. The wheel does not lose contact with the road and the road has the shape, y(d)4sin 0H(d 10) where d is distance in meters, and y(d) is the height in centimeters 1. Write the ordinary differential equation for v-1 m/s and v-5 m/s. 2. The solution of x(t)...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
Amass of m 1.78 kg connected to a spring oscillates on a horizontal frictionless surface as shown in the figure. The equation of motion of the mass is given by X = 0.303 cos(2.460) where the position x is measured in meters, the time t in seconds. Determine the period of the motion, * Tries 0/12 What is the maximum speed reached by the mass? * Tries 0/12 Determine the spring constant. BON Tring /12
show steps please
A2. A simplified car model is shown in Figure A3. It travels horizontally at a constant speed of v 20 miles perhour on a bumpy road (1 mile is approximately 1610 meters). The road surface is assumed to be rigid and has a sinusoidal profile. Both masses vibrate only in the vertical direction. m 900kg, m 60kg,k 1,000,000N/m m1 0.5 m 4k 0.1 m Figure A2. [15] [10] (1) Derive the equation of motion for the vertical...
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...
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