A 5 kilogram mass suspended from the end of a vertical spring stretches it by 1.225 metres. The system is placed in a medium offering a resistance (in Newtons) equal to 45 times the instantaneous vel...
A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 9.8 centimeters. At time ?=0 t = 0 , the resulting mass-spring system is disturbed from its rest state by the force ?(?)=150cos(10?) F ( t ) = 150 cos ( 10 t ) . The force ?(?) F ( t ) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. Solve the initial...
(1 point) A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time 0, the resulting mass- spring system is disturbed from its rest state by the force F(t) 70 cos(8t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. a. Determine the spring constant k Newtons/meter b. Formulate the initial value problem for y(), where y(t) is the displacement...
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...
(10 pts) A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass-spring system is disturbed from its rest state by the force F(t) = 170 cos(10t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. a. Determine the spring constant k. k = 1000 Newtons / meter b. Formulate the initial value problem...
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...
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.
A 20 g mass-spring system is suspended vertically. If 20 g is added, it stretches 5 cm. (Assume the mass of the spring is negligible) A) The spring constant is ________ N/m. From equilibrium position give mass-spring a speed of 1.2 m/s. B1) Period of oscillation is ______ s B2) Maximum speed of the the spring-mass system is _______ m/s. B3) The equation of motion of the oscillating spring is _______. B4) The maximum kinetic energy of the spring is...
In a hurry to digest this . Tks for the help (thumb up) 2. A mass of m kilograms (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixed to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The...
differential equations: a mass of 2kg stretches a spring 1m. the mass is in a medium that exerts a viscous resistance of 8 newtons when the velocity of the mass is 2m/sec. the mass is stretched from its equilibrium position 1m and then set in motion with a downward velocity of (3sqrt(3) - 1) m/sec. Let g=10 m/sec^2 a)state and solve the initial value problem for u(t), the displacement of the mass from its equilibrium position b) what is the...
A mass of m kilograams (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixced to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The gravitational force is mg dowswards, where g- 9.8m is acceleration due to gravity, measured...