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A mass of 1.25 kg stretches a spring 0.06 m. The...
A mass of 1.25 kg stretches a spring 0.08 mm. The mass is in a medium...
A mass of 1.25 kg stretches a spring 0.08 mm. The mass is in a medium that exerts a viscous resistance of 120 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.07 mm and released. Find an function to express the object's displacement from the spring's equilibrium position, in mm after tt seconds. Let positive displacements indicate a stretched spring,...
helpful formulas: mu’’(t)+cu’(t)+ku(t)=0 m is the mass c is the damping coefficiant k is spring constant Fd=cu’(t) k=mg/(spring displacement) A mass of 1.5 kg stretches a spring 0.08 m. The mass...
helpful formulas:
mu’’(t)+cu’(t)+ku(t)=0
m is the mass
c is the damping coefficiant
k is spring constant
Fd=cu’(t)
k=mg/(spring displacement)
A mass of 1.5 kg stretches a spring 0.08 m. The mass is in a medium that exerts a viscous resistance of 25 N when the mass has a velocity of 2 m. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.03 m and released. Find an function to express the...
ro A mass of 5 kg stretches a spring 20 cm. The mass is acted on...
ro A mass of 5 kg stretches a spring 20 cm. The mass is acted on by an external force of 10 sin N (newtons) and moves in a medium that imparts a viscous force of 4 N when the speed of the mass is 2 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 9 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8...
8. A10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg mass...
8. A10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg mass is attached to the spring, initially displaced 25 cmbelow equilibrium, and given an upward velocity of 2 m/s Find its displacement for t > 0. Find the frequency, period, amplitude, and phase angle of the motion.
Problem 5. (12 points) A mass of 5 kg stretches a spring 4 cm when hanged...
Problem 5. (12 points) A mass of 5 kg stretches a spring 4 cm when hanged vertically. Suppose that the mass is given an addition 6 cm displacement downward and then released (at time 0), and an external force of 4-3 cos(t) N at all time (starting at time 0). In addition, suppose that the mass is in a medium that exerts viscous resistance of 3 N when the mass has a velocity of 0.4 m/s. Assume acceleration due to...
A mass weighting 64 lbs stretches a spring 8 inches. The mass is in a medium...
A mass weighting 64 lbs stretches a spring 8 inches. The mass is in a medium that exerts a viscous resistance of 14 lbs when the mass has a velocity of 4 ft/sec. Suppose the object is displaced an additional 6 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) = e *'(ä сos (8.71977t) +.0167 sin(8.719771)) x cm
A 1 kg object is attached to a spring and stretches it 0.2 m on its...
A 1 kg object is attached to a spring and stretches it 0.2 m on its own. There is no damping in the system, but an external force is present, described by the function F(t) = 6 cos omega t. The object is initially displaced 30 cm downward from equilibrium with no initial velocity and system experiences resonance. Find the displacement of the object at any time t.
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a
spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
and the motion takes place in a viscous fluid that offers a
resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
A force of 720 newtons stretches a spring 3 meters. A mass of 60 kilograms is...
A force of 720 newtons stretches a spring 3 meters. A mass of 60 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion.
8. A 10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg...
8. A 10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg mass is attached to the spring, initially displaced 25 cmbelow equilibrium, and given an upward velocity of 2 m/s Find its displacement fort > 0. Find the frequency, period, amplitude, and phase angle of the motion.
helpful formulas:
mu’’(t)+cu’(t)+ku(t)=0
m is the mass
c is the damping coefficiant
k is spring constant
Fd=cu’(t)
k=mg/(spring displacement)
A mass of 1.5 kg stretches a spring 0.08 m. The mass is in a medium that exerts a viscous resistance of 25 N when the mass has a velocity of 2 m. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.03 m and released. Find an function to express the...
ro A mass of 5 kg stretches a spring 20 cm. The mass is acted on by an external force of 10 sin N (newtons) and moves in a medium that imparts a viscous force of 4 N when the speed of the mass is 2 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 9 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8...
8. A10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg mass is attached to the spring, initially displaced 25 cmbelow equilibrium, and given an upward velocity of 2 m/s Find its displacement for t > 0. Find the frequency, period, amplitude, and phase angle of the motion.
Problem 5. (12 points) A mass of 5 kg stretches a spring 4 cm when hanged vertically. Suppose that the mass is given an addition 6 cm displacement downward and then released (at time 0), and an external force of 4-3 cos(t) N at all time (starting at time 0). In addition, suppose that the mass is in a medium that exerts viscous resistance of 3 N when the mass has a velocity of 0.4 m/s. Assume acceleration due to...
A mass weighting 64 lbs stretches a spring 8 inches. The mass is in a medium that exerts a viscous resistance of 14 lbs when the mass has a velocity of 4 ft/sec. Suppose the object is displaced an additional 6 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) = e *'(ä сos (8.71977t) +.0167 sin(8.719771)) x cm
A 1 kg object is attached to a spring and stretches it 0.2 m on its own. There is no damping in the system, but an external force is present, described by the function F(t) = 6 cos omega t. The object is initially displaced 30 cm downward from equilibrium with no initial velocity and system experiences resonance. Find the displacement of the object at any time t.
A spring-mass system has a
spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
and the motion takes place in a viscous fluid that offers a
resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
8. A 10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg mass is attached to the spring, initially displaced 25 cmbelow equilibrium, and given an upward velocity of 2 m/s Find its displacement fort > 0. Find the frequency, period, amplitude, and phase angle of the motion.
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