Mechanical Vibrations (differential equations) A mass weighing 4 pounds is attached to a sping whose constant is 2lb/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point one foot above the equilibrium position with a downward velocity of 8ft/s. Determine the time at which the mass passes through the equilibrium position.

Q: A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from…

A: Solution

Q: A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of…

A: Given that  F=720 Nx=4 meters  So, the spring constant is k=Fxk=7204k=180 and, mass  m=45 kg

Q: 3. A spring with a mass of 2 kg has damping constant 14, and a force of 6 N is required to keep the…

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Q: A 2-lb weight object stretches a spring 1/2 ft. The weight is then pulled down 1/4 0, directed…

A: The given values are: w=2lbL=12ftu(0)=14ftu'(0)=0 fts-1 The differential equation would be mu''+ku=0…

Q: A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the…

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Q: velocity 4.9 m/s and initial position 9.8 m . Neglecting air resistance and A small stone is thrown…

A: Initial velocity, u=-4.9m/s (upwards)   acceleration of the stone, a=9.8m/s2    s=9.8m time taken…

Q: #3: A 70 lb weight stretches a spring 10 feet. The weight hangs vertically from the spring and a…

A: We are given the following information:Weight of springDisplacement of springDamping forceWeight is…

Q: A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the…

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Q: 01 A 500 kg satellite has been placed in a circular orbit 1500 km above the surface of the earth.…

A: give that mass of the satellite is 500kg so m=500kgthe valocity of the satellite is 30×103km/h so v=…

Q: 1) Suppose a ball is dropped from a window 20 feet above the ground. a) Find the height of the ball…

A: The distance that a free-falling object has fallen from a position of rest is also dependent upon…

Q: A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. The medium offers a…

A:

Q: A certain mass stretches one spring 3 rigid support ū k₁ m Need Help? The first mass is set aside,…

A: Solution:-

Q: 1.) The height above the ground at which a ball is released at an initial height of 122.5m is given…

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Q: 4. A spring with a mass of 3 kg has damping constant 30 and spring constant 123. (a) Find the…

A: Mass m=3 kg Dumping constant c=30 Spring constant k=123 At t=0 it starts from initial velocity2 m/s…

Q: A particle is moving with acceleration a(t) = 6t + 18. its position at time t = 0 is s(0) 13 and its…

A: Given, at=6t+8 with s0=13 and v0=2. We have to find the position at time t = 14.

Q: 3. A spring with a mass of 2 kg has damping constant 14, and a force of 6 N is required to keep the…

A: Given: A spring with a mass of 2 kg has damping constant 14, and a force of 6 N is required to keep…

Q: 3. A spring with a mass of 2 kg has damping constant 14, and a force of 6 N is required to keep the…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.