A body with mass of 500 g is attached to the end of a spring that is stretched 50 cm by a force of 36 N. At time t = 0 the body is pulled 1 m to the right, stretching the spring, and set in motion with an initial velocity of 9 m/s to the left. (a) Find x(t) in the form C cos (@ot-a). (b) Find the amplitude and the period of motion of the body. (a) x(t) = (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.)

What is the period of small oscillations for a simple pendulum of length L=4 m if it is placed in a car that is accelerating horizontally at 4m/s2?

The position of an object in harmonic motion on the end of a spring is p=    2 cos(3t)- 4sin(3t),where is measured in seconds and is measured in inches. What is the velocity (in in/s) of the object at t= pi/3 seconds?

Problem 9: An ideal pendulum of length L=1.1 m supports a mass of m =0.5 kg. Initially the pendulum is lifted such that it makes an angle of 0 = 26 degrees with respect to the vertical. m 10

What is the period of small oscillations for a simple pendulum of length L=4 m if it is placed in a car that is accelerating horizontally at 4m/s2?

(a) Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.)   (b)Write an equation that represents the curve in the form

(B) llllllll Students set up an experiment by attaching an ideal vertical spring to a support and hanging a block of known mass from the spring. The students pull the block down and release it from rest. The students then measure the period of the block's oscillation. This procedure is repeated for several trials using the same spring but with blocks of different known masses. The students are instructed to create a linear graph using the mass m of each block and the period T of the block's motion. The slope of the graph will be used to calculate the force constant k of the spring. Which of the following best indicates how the students should create their linear graph and how k can be calculated from the slope of the graph? E k Graph T on the vertical axis and m on the horizontal axis; set k = 2π slope Graph T² on the vertical axis and m on the horizontal axis; set k Graph T on the vertical axis and m² on the horizontal axis; set k Graph T² on the vertical axis and m on the horizontal…

The following given is for questions 3 and 4: A block of mass m = 2 kg is attached to a spring with spring constant k = 200 N/m, and set to oscillates on a frictionless horizontal surface. At time t = 0 its position is xo = 0 and its velocity is vo = +5 m/s. 3) Which of the following is true about the oscillation amplitude and the phase constant, p: (a)A = 0.5, p=7/2 (b)A = 0.5, p=-7/2 (c) A = 0.25, p= t/2 (d)A = 0.25, p=-r/2

The displacement of a particle in motion is given by x= a sin ot + b cos ot meter where a, X = b and o are constants. Show that the motion is simple harmonic. If a = 3 cm, 3 ст, b = 4 cm, o = 2 rad/s, find the period, maximum %3D velocity and maximum acceleration.

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