Problem 5: A mass m = 1.81 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant k = 86 N/m and negligible mass. The mass undergoes simple harmonic motion when placed in vertical motion. At time t= 0 the mass is observed to be at a distance d = 0.55 m below its equilibrium height with an upward speed of vo = 4.1 m/s. ► Determine the phase angle of the motion, in radians. ) Determine the amplitude of the motion, in m. Determine the distance from equilibrium, in m, when the mass moves with a speed half its initial speed.

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 BA A 100 g 100 g C At what point will the system have the largest total energy? O A В C All points will have the same amount of total energy.

An object weighing 4 kg, one end of which is connected to the other end of a spring connected to the ceiling, makes an oscillating movement in a frictional environment. It is known that the friction force is proportional to the speed of the object and its proportionality coefficient is 5 Ns/m and the spring constant is 0.2 N/m. At t = 0, the object starts to move after being raised 2 m upwards from the equilibrium position, and it is known that it passes 5 m below the equilibrium position at t = 10 s. Write the differential equation that describes the motion of the object and then find the equation that relates the position of the object to time.

A mass weighing 2lb stretches a spring 6in. If the mass is pulled down an additional 3in and then released, and if there is no air resistance, find the natural frequency, period and amplitude of the motion. O Natural frequency w = 8 rad/sec, Period T = sec, Amplitude R ft Natural frequency w = = 4 rad/sec, Period T = sec, Amplitude R ft O Natural frequency w = 8 rad/sec, Period T = sec, Amplitude R = ft 1 O Natural frequency w = 8 rad/sec, Period T = sec, Amplitude R = ft 8

A 0.23 kg mass is suspended on a spring which stretches a distance of 5.3 cm. The mass is then pulled down an additional distance of 11 cm and released. What is the displacement from the equilibrium position with the mass attached (in cm) after 0.33 s? Take up to be positive and use g = 9.81 m/s2. The initial condition should be set as y(0)=-A because the mass is pulled below the equilibrium (the origin along y-axis) and released. Hint: Get k from the displacement as it was done in this example. The equation will have ω = (k/m)1/2, and the phase will be such that it will be a cosine with a negative amplitude, because it starts at a negative displacement.

A 16 kg weight is attached to a spring with constant k = 144 kg/m and subjected to an external force F(t) = 160 sin(2t). The weight is initially displaced 3 meters above equilibrium and given an upward velocity of 3 m/s. Find its displacement for t > 0, with y(t) measured positive upwards. y(t) =

During an experiment, a student tests a spring's oscillation period with different masses. The testing masses are 50g, 100 g, 200 g, and 500 g. Which of the following statements is correct? The 100 g has the highest frequency. The 500 g has the highest frequency. The 50 g has the highest frequency. O The 200 g has the highest frequency.

An initially 'un-compressed' spring (x1=0) is observed to compress 0.4 m before stopping and reversing the 26 m/s horizontal velocity of a 100 kg mass. Determine the spring constant in N/mm.