A massless spring of spring constant 395 N/m is submerged in a viscous fluid wit damping constant b = 19 kg/s. A 4.8-kg block is attached to the spring, stretched 0.650 meters, and released from rest. The mass then begins to oscillate harmonically with a resistive force proportional to the speed of the mass. a. Write the position function for this motion with values for A, w', and y. b. Calculate the time when the amplitude is 60% of its maximum value. c. Is this an example of a critically damped, overdamped, or underdamped system Explain.

8. A weight of 0.5kg stretches a spring by 0.49m. The spring-mass system is submerged in delicious melted butter with a damping coefficient of y=4. The spring is then lowered by an additional 1.0m and released with velocity 0. There is no external force. Find the function which gives the location of the weight at time t. Note: I have designed this to work out nicely. If it's not working out nicely then you probably got some butter in your calculations.

The motion of a particle is given by x = A sin3(ωt). a. Enter an expression for the amplitude of the particle's motion.  b. Enter an expression for the particle's velocity, v.  c. Enter an expression for the particle's acceleration, a.

Problem 9: A 12.0-g bullet is fired into a block of wood (at rest) with some initial speed. The block is attached to a spring that has a spring constant of 200 N/m and rests on a frictionless floor. The block with the embedded bullet oscillates at a frequency of f= 2.8 Hz and compresses a maximum distance of d = 0.51 m. What was the initial speed of the bullet? d

Problem HW7.2 A block of mass m = 1.8 kg is fastened to an unstrained horizontal spring whose spring constant is k = 85 N/m. The block is given a displacement of +0.15 m, where the sign indicates that the displacement is along the +x-axis, and then released from rest. (a) Find the angular frequency of the resulting oscillatory motion. Does this number change if the initial displacement is larger? Explain with a sentence or two. (b) Use concept of energy to determine the maximum speed of the block. Explicitly state which initial and final positions you used for energy states. (c) Use the concept of force to set up a free body diagram and Newton's Second Law equation to determine the magnitude of the maximum acceleration of the block.

B5

A mass of 1.64 Kg is connected to a spring of spring constant 9.02 N/m. An oscillation is started by pulling the mass to the right to amplitude 0.779 m before release and the oscillator moves in air. The oscillation decays to 16.7% of the original amplitude in 63.5 seconds.   a.  What would the position of the oscillation be 29.63 seconds after release?

A 330-kg wooden raft floats on a lake. When a 70-kg man stands on the raft, it sinks 3.9 cm deeper into the water. When he steps ff, the raft oscillates for a while. Part A What is the frequency of oscillation? Express your answer using two significant figures. Η ΑΣφ Hz Submit Request Answer Part B What is the total energy of oscillation (ignoring damping)?

A thin metal disk mass 2.00×10^(−3)kg and radius 2.20 cm is attached at its center to a long fiber (Figure 1). The disk, when twisted and released, oscillates with a period of 1.00 s. Find the torsion constant of the fiber. Express your answer in N⋅m/rad.

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