The force of a spring is given by F = −kx, where k is the stiffness of the spring and x is the displacement of the spring from equilibrium. From an earlier activity, we said that the derivative of the potential energy with respect to position is equal to the negative force. Assume that at equilibrium (when x = 0), the spring has no potential energy. (a) Write an initial value problem for solving P E(x). Clearly identify the initial condition.

Q: A particular spring does not obey Hooke’s law (F(x) = - k x), but rather is described by F(x) = -…

A:

Q: A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass…

A: a. Draw the free-body diagram of the mass m.

Q: h one end of a spring with a force constant k = 753 N/m to a wall and the other end to a mass  m =…

A: Givenk=753 N/mm=1.42 kgxi=6.56 cm=0.0656 m

Q: A horizontal spring with force constant  k = 630 N/m  is attached to a wall at one end and to a…

A: The given values are, k=630 N/mm=2.45 kgx=4.00 cm=4.00×10-2 mμk=0.300

Q: A spring with a spring constant of 150 N/m and an attached mass of 2 kg has an initial position of…

A:

Q: A 2 kg block is released from rest at position 1, slides down a frictionless curve, proceeds on a…

A: As energy cannot be created or destroyed, it can only be transferred from one form to another.…

Q: Hooke's law describes a certain light spring of unstretched length 34.2 cm. When one end is attached…

A: The spring constant, k=Fx=mgl'-l   Substitute, k=6.75 kg9.8 m/s240.4 cm-34.2 cm=1066 N/m=1.066 kN/m

Q: A horizontal spring with force constant k = 680 N/m is attached to a wall at one end and to a…

A:

Q: A pendulum is lifted to a certain height and then released, which causes the pendulum to swing back…

A: The total energy relation is given as TEi=TEfPEi+KEi=PEf+KEfmgh+0=0+12mv2mgh=12mv2 The potential…

Q: A spring with spring constant k = 80 N/m has an equilibrium length of 1.00 m. The spring is…

A:

Q: As seen in Fig. 1, a 5.00 kg mass starts from rest at the top of a frictionless incline at heighty0=…

A:

Q: If possible, express your final answer in the form u(1) = Rcos(@,t – 8). 4. A 10-kg mass is attached…

A:

Q: An object, whose mass is 0.480 kg, is attached to a spring with a force constant of 110 N/m. The…

A: Given data: Mass (m) = 0.480 kg Spring constant (k) = 110 N/m Amplitude (A) = 0.120 m Required: The…

Q: Consider the spring mass system shown below. The natural frequency of the system is 4rad/s for a…

A: The time period of spring mass system is given by the formula T=2πmkequivalent

Q: u have two equal masses m1 and m2 and a spring with a spring constant k. The mass m1 is connected to…

A: Given :- The mass m1 = m2 = 0.340 kg. The spring constant k = 230 N/m. You now pull the mass m2 down…

Q: A horizontal spring-mass system has low friction, spring stiffness 220 N/m, and mass 0.4 kg. The…

A:

Q: An air glider of mass m = 0.500 kg is on a level air track and connected to a massless ideal spring…

A:

Q: A spring with a constant of 730 N/m is compressed by a block of mass m = 1.2 kg. When the block is…

A: m = 1.2 kg k = 730 N/m L = 0.05 m coefficient of kinetic friction = 0.44 v = 2.3 m/s Using equation…

Q: A horizontal block-spring system with the block on a frictionless surface has total mechanical…

A: As per our guidelines, we only answer one question per session with maximum of three subparts. As,…

Q: Problem: An object of mass m=0.20 kg is suspended from the ceiling on a spring of relaxed length 40…

A: a) Let the equilibrium be after spring elongates ∆y. At this position we have,…

Q: A system, consisting of a mass M connected to a spring, oscillates on a frictionless surface with…

A: Ans. (C) neither O, X nor Y

Q: A body of mass m = 2,50 kg is hung on a vertical spring of spring constant k = 90 N/m. At t = 0 the…

A:

Q: A 0.033kg block on a frictionless horizontal surface is attached to a 130N/m spring. The block is…

A: The spring constant is, k=130 N/m The amplitude of the system is, A=0.08 m The block's mass is,…

Q: At t = 0 a block with mass M = 4 kg moves with a velocity v = 3 m/s at position x, = -.33 m from the…

A: Given that:Mass of the block, M=4 kgInitial velocity, v= 3 m/sInitial displacement, xo=-0.33 mSpring…

Q: You have two equal masses m1 and m2 and a spring with a spring constant k. The mass m1 is connected…

A: Note: As per the guidelines, we can only answer three subparts of a question. Sorry for the…

Q: A solid tungsten block of mass m is pressed against a spring of force constant k. As a result, the…

A: Given : Mass of the block  = m Force constant of spring  =  k Compressed distance of the spring  =…

Q: ( ANSWER e,f, and g ), a is given ) You have two equal masses m1 and m2 and a spring with a…

A: Given: The mass m1 = m2 = 0.500 kg. The spring constant k = 290 N/m. You now pull the mass m2 down a…

Q: A light spring with a spring constant k = 370 N/m is attached to a vertical wall at one end and a…

A:

Q: A spring 1.50 m long with force constant 442 N/m is hung from the ceiling of an elevator, and a…

A: a. the force applied on the sample will be equal to the negative of the restoring force, so…

Q: (b) A block of mass, m = 0.40 kg is attached to a spring with force constant, k= 2.5 Nm' and damping…

A: Given:  x(t) = Ae-b2mtsinωt+φ0b = 0.56 kg/secm = 0.4 kgk = 2.5 N/mAt t =0, v = -0.6 m/s

Q: A 150 g glider on a horizontal, frictionless air track is attached to a fixed ideal spring with…

A:

Q: A simple harmonic oscillator consists of a 2 kg block attached to a horizontal spring (k=800 N/m).…

A: Given data: The mass of the block is, m=2 kg. The horizontal spring having the spring constant is,…

Q: B/ A copper spring with elastic constant of 28 N/m was placed horizontally and attached to a mass of…

A: Given Spring constant k=28N/m Mass m=0.25kg Amplitude A=0.06m

Q: The block of mass m = 1.60 kg slides along the horizontal rough plane as shown in the figure. The…

A: Given information: The mass of the block (m) = 1.60 kg The stiffness of the of the spring (k) = 30…

Q: A spring 1.50 m long with force constant 460 N/m is hung from the ceiling of an elevator, and a…

A:

Q: A horizontal spring system consists of a block of mass 4.25 kg on a frictionless surface attached to…

A: a) When a spring is displaced by a distance x from its equilibrium position then the force acting on…

Q: A particle with a mass of 0.500 kg is attached to a horizontal spring with a force constant of 50.0…

A: Given data: The mass of a particle is: m = 0.5 kg The angular frequency is: ω The force constant is:…

Q: A mass of m = 200 g is attached to the end of a spring whose mass is negligible, with spring…

A:

Q: The motion of a particle is given by x(t) = (25 cm) cos(18t), where t is in s. Part A What is the…

A: Given, The equation, governing the motion of a particle is :  x(t) =(25cm) cos (18t) We have to find…

Q: A block of mass m = 2.00 kg is attached to a spring of force constant k = 4.35 x 102 N/m that lies…

A:

Q: A spring of negligible mass stretches 3.46 cm from its relaxed length when a force of 5.4 N is…

A: The stretch of the spring is x = 3.46 cm = 0.0346 m. The applied force F = 5.4 N. The mass of the…

Q: A particle with a mass of 0.500 kg is attached to a horizontal spring with a force constant of 50.0…

A:

Q: A block on a horizontal surface is attached to a horizontal spring of negligible mass. The other end…

A: The total energy of simple harmonic motion is equal to its kinetic energy of motion and potential…

Q: hung from an ideal spring (its length is equal to zero and no friction) and reaches equilibrium at…

A:

Q: A spring 1.50 m long with force constant 428 N/m is hung from the ceiling of an elevator, and a…

A: Using Hooke's law, the restoring force F=-kx   The force on the sample, F=mg

Q: A mass of 0.8 kg is attached to a horizontal spring whose stiffness is 10 N/m. Friction is…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest.