A spring is stretched 12 inches by a 24-pound weight. If the weight is pulled 10 inches below the equilibrium position and released with a downward velocity of 6ft/sec, find the position of the weight at any time t.

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A: therefore Estimate of velocity is 201.34 +- 0.7

Q: A spring has natural length 27 cm. Compare the work (in J) W, done in stretching the spring from 27…

A: So  W1 = 4k125 J

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Q: Compute the work required to stretch a spring from 7 to 14 cm past equilibrium, assuming that the…

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Q: A heavy-duty shock absorber is compressed 2 cm from its equilibrium position by a mass of 500 kg.…

A: Let K be spring constantThen ,Kx2x10-2=500x9.8⇒K=245000 N/m

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Q: A 5-kg mass is attached to a spring whose stiffness constant is 80 N/m. The damping is negligible.…

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Q: After a 10-lb weight is attached to a 5-ft spring, the spring measures 7 ft long. The 10-lb weight…

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Q: With what initial velocity v0 must we fire a rocket so it attains a maximum height r above the…

A: We will use the maximum height formula Where u=initial velocity. g=gravity H_max= maximum height

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A: Given, Velocity of the particle = v(t) = 4 - 2t  We have to find the displacement at time t = 2 So,…

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A: Definition used -                   v=∫adts=∫vdt

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A: Given Data: The constant acceleration is: a The initial velocity is: v0 The initial displacement is:…

Q: The value of the instantaneous velocity at t = 1 is

A: Consider the position function To calculate the instantaneous velocity

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A: To determine the velocity of the object.

Q: Given the following acceleration function of an object moving along a line, find the position…

A: Given,  at = -24 v0 = 19 s0 = 0  We have the position function st.

Q: A 5 kg weight is attached to a spring with constant k = 80 N/m and subjected to an external force…

A: Consider my¨+ky=Ft......1 Given that m=5 kg, k=80 Nm and Ft=140sin3t..…

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Q: A mass weighing 64N stretches a spring 0.32 m. The mass is initially released from a point 8 m above…

A: Given, a mass weighing 64N stretches a spring 0.32 m. The mass is initially released from a point 8…

Q: A 20-lb weight is hung on an 18-in. spring stretching it 6 in. The weight is pulled down 5 in. and 5…

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Q: Compute the work required to stretch a spring from 7 to 13 cm past equilibrium, assuming that the…

A: Given query is to find the the work required.

Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: A mass weighing 64 N stretches a spring 0.32m. The mass is initially released from a point 8m above…

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Q: A mass weighing 64N stretches a spring 0.32 m. The mass is initially released from a point 8 m above…

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Q: A 3 kg mass is attached to a spring with stiffness k = 48N / m. The mass moves 1/2 m to the left of…

A: The equation can be given as; y" + (k/m)y =0,   The mass moves 1/2 m to the left of the equilibrium…

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Q: An 80-lb weight is attached to the lower end of a coil spring suspended from the ceiling and having…

A: We have given that the spring constant (k)=62.6 lb/ft, weight =80 lb and mass=8032=2.5 lb s2/ft We…

Q: It takes 1,600 joules (J) of work to stretch a spring from its natural length of 4 meters (m) beyond…

A: W=12kA2, where A is stretched or compressed length of spring

Q: Consider the following system: A 3lb weight on a spring stretches it 6 inches. Assuming a damping…

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Q: Suppose that a particle moves along a straight line with velocity defined by v(t) = t 2 – 3t – 18,…

A: Given,           Suppose that a particle moves along a straight line with velocity defined by…

Q: A mass-spring system is subjected to a single external force F (t) = sin (t), which acts for 0≤t≤2π…

A: Given mass-spring system is subjected to a single external force F (t) = sin (t), which acts for…

Q: If f(t)=2t+sin(t) describes the length of an oscillating spring in m/s, what is the instantaneous…

A: Solution is written in below steps.

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A: We know that the rate of change of velocity of a moving particle is known as its acceleration. Let…

Q: A spring is stretched 4 in. by a 2-lb weight. The 2-Ib weight is started from the equilibrium point…

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Q: It takes 50J of work to stretch a spring 0.2m from its equilibrium position. How much work is needed…

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Q: A 0.5 kg mass is attached to a spring having a spring constant of 8 N/m. The mass is set into motion…

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Q: A spring is stretched 6 in. when a 4-lb weight is hung on it. The 4-lb weight is attached and pushed…

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Q: A train moves at a velocity of v(t)= 3t" - 3200t km/sec where t in seconds is the time passed since…

A: Find your answer below

Q: Suppose an object moves along a line at 19 m/s for 0sts2 s and at 25 m/s for 2<ts5 s. Sketch the…

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Q: What is the position at time t of a car that is accelerating at a rate of 5 meters per second…

A: To determine the position of the car from the given data. (note that s =20 when t=2, not as given)

Q: Suppose a force of 30 N is required to stretch and hold a spring 0.1 m from its equilibrium…

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Q: It takes 15 J of work to stretch a spring 0.2 m from its equilibrium position. Find the spring…

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Q: If the velocity function v(t) of an object is at its maximum, then the value of a(t), its…

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