Spring with a force constant of 25.0 N/m oscillates with an amplitude of 7.00 cm on a frictionless, horizontal surface. (a) Find the total energy of the system. m3 (b) Find the speed of the object when its position is 1.15 cm. (Let o cm be the position of equilibrium.) m/s (c) Find the kinetic energy when its position is 3.00 cm. m) (d) Find the potential energy when its position is 3.00 cm. m)

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Solve C

A 6-g object connected to a spring with a force constant of 7 N/m oscillates with an amplitude of 6 cm on a frictionless, horizontal surface. Find the potential energy when its position is 3 cm. (answer should be in 3 decimal places)

A 2.0-kg cart attached to a spring undergoes simple harmonic motion so that its displacement is described by x = (0.20 m)sin[(2π/2.0 s)t]. Construct energy bar charts for the cart-spring system at times t = 0, t = T/4, t = T/2, t = 3T/4, and t = T.

The potential energy of a spring is given by U(x) = (8x²-5x-4)J if x is given in metres. What is the equilibrium length of the spring? x= number (rtol=0.05, atol=1e-08) m

Q3 (a) (b) (c) (d) Sketch the following against time for a simple mechanical oscillator: (i) The displacement of the mass. (ii) The potential energy of the mass. (iii) The kinetic energy of the mass. Briefly explain the difference between the instantaneous power and average power of a mechanical oscillator. A mass of 120 g is displaced from its equilibrium position by a distance of 32 cm when a force of 50 N is applied to it. When the force is removed at time, t= 0 s, the mass begins to oscillate. At at time, t = 4.5 s, the peak amplitude of the oscilliations of the system is reduced to 0.368 times the amplitude when t=0 s. Calculate: (i) (ii) (iii) (iv) The spring constant of the system The total energy of the system at t=0 s The total energy of the system at t = 4.5 s The quality factor of the system Sketch both the displacement and the instantaneous power of the mass against time for a simple mechanical oscillator.

5. 0 m feeeee A mass m = 25 kg is sitting on a slope with = 20°. There is no friction between the mass and the slope. The mass is attached to a spring with rest length lo = 5 cm that is mounted at the top of the slope. When the mass is released, the spring stretches an amount Ax = 6.2 cm (as measured along the slope, total length is now 11.2 cm) when the system reaches static equilibrium. a.) Draw the free-body diagram of the mass, showing all forces acting on the mass. b.) Calculate the value of the spring constant, k.

A horizontal spring on a frictionless surface with a spring constant of 50 N/m is compressed 0.4 m away from equilibrium and it is held at rest. A 5 kg mass is attached at the end of the spring. The spring-mass system is released from rest. Calculate the kinetic energy of the mass when it is halfway back to its equilibrium position (0.2 m away).

QUESTION 4 Q 4(a) The force, F, required to compress a spring is given by F = 1000x + 50x³, where x is displacement from its unstretched length. The work done, W, to compress a spring by 0.3m is given by 0³ F dx. Determine W, giving your answer correct to 2 significant figures. Q 4(b) The velocity, v, of a piston moving with simple harmonic motion at time, t, is given by v = 20sin (3t) Find in terms of TT, the mean velocity between t = 0 and t = =F Q 4(c) Sketch the region bounded by the curve f(x) = and the line g(x) = 3 - x, for 0 ≤ x ≤ 3. Use integration, determine the area enclosed by the curves, giving your answer correct to 4 decimal places.