2. A spring is stretched 10 mm by a 10 g of mass. The mass is pulled an additional 6 mm and released. Determine the position u as a function of time. Write your solution in the form u(t) = Rcos(wt-6) (Ignore damping and g = 9.8m/s².)
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- 32. A 100 gram mass is attached to a spring and undergoes simple harmonic motion with period of T=2 sec. If the total energy of the systenm is E= 5J, find (a) force constant k. and (b) the amplitude of motion 4.0. A mass of 0.42 kg, attached to a horizontal ideal spring of force constant 38 N/m, undergoes simple harmonic without friction at an amplitude of 5.3 cm. (a) What total distance does mass cover during a single oscillation? [ANS: 21.2 cm] (b) What is the maximum energy of the mass - spring system? [ANS: 0.053 J] ( c) Determine the maximum speed of the mass? [ANS: 0.50 m/s] (d) What is the speed of the mass when the displacement is 4.0 cm? [ANS: 0.33 m/s]
- An ideal spring hangs from the ceiling. A 1.25 kg mass is hung from the spring, stretching the spring a distance d = 0.0865 m from its original length when it reaches equilibrium. The mass is then lifted up a distance L = 0.0325 m from the equilibrium position and released. What is the kinetic energy K of the mass at the instant it passes back through the equilibrium position? K = d Equilibrium position wwwwww. www6. A 2.0 kg mass attached to a 24.0 N/m massless spring is driven by an external force F = F, cos (2nt) where Fo= 12.0 N. Assuming that the damping coefficient b is so small that it can be neglected, find a) the period of the oscillator, and b) the amplitude of its motion.Consider an ideal spring with spring constant k = 20 N/m. The spring is attached to an object of mass m = 2.0 kg that lies on a horizontal frictionless surface. The spring-mass system is compressed a distance xo = 50 cm from equilibrium and then released with an initial speed vo= 0 m/s toward the equilibrium position. x=0 equilibrium initial state a. What is the period of oscillation for this system? b. Starting at t = 0, how long will it take for the object to first return to the equilibrium position?
- A spring of force constant K attached to the wall on a horizontal smooth plane. The sprıng is compressed by a block of mass 6 kg a dstance x= 0.2 The speed of the block as it released and passes the equilibrium position is 2 m/s. Find the force constant k (in N/m). 00000 mo0000000007. A 0.250 kg block oscillates on a spring horizontally on a frictionless surface. The spring has a spring constant of 200 N/m. The amplitude of the oscillations is 24.5 cm. a. What is the period of this mass-spring system (in seconds)? b. What is the maximum speed of the block (in m/s)?1. A pendulum of length L = 0.80 m is released from B with a speed of 1.0 m/s as shown in the figure. Find the speed of the pendulum at the lowest point c. 30° B C