Displacement (m) 1.04 。 -1.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Time(s)
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- A mass m = 0.5 kg slides on a frictionless plane attached to a spring with spring constant k = 100 N/m and undergoes SHM(simple harmonic motion). Its position x(t) = 0.1cos(ωt +π/4) m, where ω =sqrt(k/m). i. What is the initial position of the mass? ii. Write the speed of the mass as a function of time. What is the maximum speed? iii. What is the total energy of this oscillator?bA particular spring does not obey Hooke’s law (F(x) = - k x), but rather is described byF(x) = - k1 x - k2 x2.x is the displacement of the spring from equilibrium and the constants k1 and k2 are given below.Randomized Variablesk1 = 6.9 N/mk2 = 6.7 N/m2 Part (a) Input an expression for the potential energy of the spring as a function of position. Assume that U(0) = 0. Part (b) What is the magnitude of the restoring force of this spring, in newtons, if it is stretched 28 cm from equilibrium?
- A 1.10 kg block is attached to a horizontal spring with spring constant 2200 N/m. The block is at rest on a frictionless surface. A 11 g bullet is fired into the block, in the face opposite the spring, and sticks. Part A What was the bullet's speed if the subsequent oscillations have an amplitude of 10.7 cm ? Express your answer to two significant figures and include the appropriate units. 28 = Submit μA Value Request Answer Units ?A person exerts a 15N force on a cart attached to a spring and holds the cart steady. The cart is displacement 0.060m from its equilibrium position. When the person stops holding the cart, the system cart+spring undergoes simple harmonic motion. (22) a. Determine the spring constant of the spring b. Determine the energy of the system. c. Write expressions x(t), v(t), and a(t) for the cart.Near the top of the Citigroup Center building in New York City, there is an object with mass of 3.2 × 105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. A. What effective spring constant should the springs have to make them oscillate with a period of 2.2 s in N/m? B. What energy is stored in the springs for a 1.4 m displacement from equilibrium in J?
- A spring mass system consists of a spring with spring constant k and an attached block of mass m is submerged in a liquid that produces a damping force F, . m = 1 Kg F, = 10 times the instantaneous velocity of the center of mass of the block. k = 16 N/m If the mass is initially released from rest 1 meter below the equilibrium position. a. Give a second degree equation that describe the motion of the center of mass of the attached block b. Solve the equation in part a.A mass m = 3.3 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A = 4.5 cm and a frequency f = 1.5 Hz. a. Write an equation for the spring constant k. b. Calculate the spring constant k, in Newtons per meter. c. Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement. d. Calculate the total mechanical energy E, in joules.A mass of 240 g oscillates on a horizontal frictionless surface at a frequency of 2.5 Hz. a. What is the effective spring constant for this motion?
- The collar of negligible size has a mass of 0.25 kg and is attached to a spring having an unstretched length of 100 mm. If the collar is released from rest at A and travels along the smooth guide, determine its speed just before it strikes B. 400 mm k = 150 N/m 200 mmDon't use chat gptA block on a horizontal surface is attached to a horizontal spring of negligible mass. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. The block-spring system is then placed into simple harmonic motion. The figure shows a graph of the velocity of the block as a function of time. At which of the following times does the block-spring system have maximum spring potential energy? A.1.5 s B.2.5 s C.2 s D.4.5 s