An object executes simple harmonic motion with an amplitude A. (Use any variable or symbol stated above as necessary.) (a) At what values of its position does its speed equal half its maximum speed? x = ±        (b) At what values of its position does its potential energy equal half the total energy? x = ±

Questions 2-5 reference the picture of mass attached to a spring shown. The left most picture gives the spring in its relaxed (equilibrium) position. The mass is lifted to point "B" and let go such that it oscillates up and down as shown in the right most position. Positions B and C are its highest and lowest points while bouncing. Point A is where the mass is traveling the fastest. Neglect air drag. 100 g B A 100 g 100 g At what point will the mass have the largest elastic (spring) potential energy? A В C All points will have the same amount of elastic potential energy. hllll

A spring hangs vertically from a ceiling. The spring constant of the spring is k=15 N/m. A 2kg object has been attached to the spring and the spring has already come to its new equilibrium. Someone pulls the object down by 5cm and releases it at time t = 0s. The spring and object begin to oscillate under simple harmonic motion. Find the total energy of the system, the maximum kinetic energy, the maximum potential energy, and the positions where the maximum energies occur.  Answers: 0.01875 J, 0.01875 J

A mass of 1kg is attached to a spring with a spring constant of k=10 N/m. you stretch the spring to distance A from equilibrium and let go. The mass oscillates with a certain period, frequency, and total energy. Now stretch the spring to a distance of 3A. compared to the original total energy E, what is the new total energy of the system now?

A mass m is attached to a spring of force constant 76.0 N/m and allowed to oscillate. The figure (Figure 1) shows a graph of its velocity vx as a function of time t. Find the period, frequency, and angular frequency of this motion. What is the amplitude (in cm)? At what times does the mass reach the position x=±A in the interval between t=0s and t=1.8s including the endpoints? Find the maximum acceleration of the mass. Find the times at which the maximum acceleration occurs in the interval between t=0s and t=1.8s including the endpoints. What is the mass m?

For a simple harmonic oscillator with x=Asinωtx=Asin⁡ωt write down an expression for the velocity. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate (without the quotes). For trigonometric functions use the usual sin and cos, while for Greek letters such as ωω, use omega.

Please answer questions 3, 4 and 5! A 780 g object is hung from a spring with a force constant of 30 N/m. What is the displacement of the spring from equilibrium length if it is hanging vertically Now, the mass in question a is being pulled downward by an additional 9 cm. What is the potential energy? You release the object, what is the period of oscillation of the mass/spring system?  Using yt=Acos(wt), what is the expression of the vertical motion along the y-axis?  What is the maximum speed of the oscillating object? What is the maximum kinetic energy? Do these values make sense from the values in part b?

Questions 2-5 reference the picture of mass attached to a spring shown. The left most picture gives the spring in its relaxed (equilibrium) position. The mass is lifted to point "B" and let go such that it oscillates up and down as shown in the right most position. Positions B and C are its highest and lowest points while bouncing. Point A is where the mass is traveling the fastest. Neglect air drag. 100 g B A 100 g 100 g At what point will the mass have the most kinetic energy? A В C All points will have the same amount kinetic energy.