The pendulum swings with a frequency of 0.49 Hz and an amplitude of 0.05 radians. Determine the maximum speed of the swinging bob whose mass is 50 lb. (assume phase angle = 0).

We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.

For each expression, identify the angular frequency , period T, initial phase and amplitude ymax of the oscillation. All values are in SI units. a. y(t) = 0.75 cos (14.5t) b. vy (t) = 0.75 sin (14.5t + /2) c. ay (t) = 14.5 cos (0.75t + /2) 16.3

A vibration sensor, used in testing a washing machine, consists of a cube of aluminum 1.50 cm on edge mounted on one end of a strip of spring steel (like a hacksaw blade) that lies in a vertical plane. The strips mass is small compared with that of the cube, but the strips length is large compared with the size of the cube. The other end of the strip is clamped to the frame of the washing machine that is not operating. A horizontal force of 1.43 N applied to the cube is required to hold it 2.75 cm away from its equilibrium position. If it is released, what is its frequency of vibration?

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 46.0 cm. The explorer finds that the pendulum completes 96.0 full swing cycles in a time of 145 s. What is the magnitude of the gravitational acceleration on this planet? Express your answer in meters per second per second. If we use idea of simple pendulum, such that the period or T = square root of the length/g cycles, I believe that 2 pie when when get rid of square root makes 2 pie become 4 pie.  Please the math steps in detail where g= 4pie^2/T^2 I need to get the steps right, so I can use 2pie*sqare riit if L/G

This time the pendulum is 2.42 m long. Suppose you start with the pendulum hanging vertically, at rest. You then give it a push so that it starts swinging with a speed of 2.68 m/s. What maximum angle (in degrees) will it reach, with respect to the vertical, before falling back down?     41.5 degrees     36.7 degrees     31.9 degrees     16.0 degrees

Orangutans can move by brachiation, swinging like a pendulum beneath successive handholds. If an orangutan has arms that are 0.90 m long and repeatedly swings to a 20° angle, taking one swing immediately after another, estimate how fast it is moving in m/s.

At what angle does the tension in the 0.6 m long pendulum cord become zero if the 1.0 kg pendulum has a speed of 5.0 m/s at its lowest point (when θ=0o)?

A mass m = 6.6 kg hangs on the end of a massless rope L = 2.04 m long. The pendulum is held horizontal and released from rest. Now a peg is placed 4/5 of the way down the pendulum’s path so that when the mass falls to its vertical position it hits and wraps around the peg. As it wraps around the peg and attains its maximum height it ends a distance of 3/5 L below its starting point (or 2/5 L from its lowest point).   1. How fast is the mass moving at the top of its new path (directly above the peg)? m/s     2) Using the original mass of m = 6.6 kg, what is the magnitude of the tension in the string at the top of the new path (directly above the peg)? N

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