BackA diving board oscillates with simple harmonic motion of frequency 3.0 cycles per second. What is the maximum amplitude with which the end of the board can oscillate in order that a pebble placed there (Fig. 14–42) does not lose contact with the board during the oscillation?
(II) A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end of the spring is fixed to a wall. It takes 3.2 J of work to compress the spring by 0.13 m. The mass is then released from rest and experiences a maximum acceleration of 12m/s². Find the value of the mass.
Draw a graph like Fig. 14–11 for a horizontal spring whose spring constant is 95 N/m and which has a mass of 75 g on the end of it. Assume the spring was started with an initial amplitude of 2.0 cm. Neglect the mass of the spring and any friction with the horizontal surface. Use your graph to estimate the speed of the mass, for 𝓍 = 1.5 cm.
If the amplitude of a simple harmonic oscillator doubles, what happens to its total mechanical energy?
A block of mass 0.300 kg is attached to a spring. At x = 0.240 m, its acceleration is ax= -12.0 m/s2 and its velocity is vx=4.00 m/s. What are the system's (a) force constant k and (b) amplitude of motion?
A 500 g air-track glider attached to a spring with spring constant 10 N/m is sitting at rest on a frictionless air track. A 250 g glider is pushed toward it from the far end of the track at a speed of 120 cm/s. It collides with and sticks to the 500 g glider. What are the amplitude and period of the subsequent oscillations?
(I) A 1.28-kg mass oscillates according to the equation 𝓍 = 0.650 cos7.40 t where 𝓍 is in meters and t in seconds. Determine the total energy.
A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute the speed of the glider when it is at x = -0.015 m.
A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end of the spring is fixed to a wall. It takes 3.2 J of work to compress the spring by 0.13 m. The mass is then released from rest and experiences a maximum acceleration of 12m/s². Find the value of the spring constant.
For the ground level of a harmonic oscillator, . Do a similar analysis for an excited level that has quantum number . How does the uncertainty product depend on ?
A cheerleader waves her pom-pom in SHM with an amplitude of 18.0 cm and a frequency of 0.850 Hz. Find (a) the maximum magnitude of the acceleration and of the velocity; (b) the acceleration and speed when the pom-pom's coordinate is x = +9.0 cm; (c) the time required to move from the equilibrium position directly to a point 12.0 cm away. (d) Which of the quantities asked for in parts (a), (b), and (c) can be found by using the energy approach used in Section 14.3, and which cannot? Explain.
A pinball machine uses a spring launcher that is compressed 6.0 cm to launch a ball up a 22° ramp. Assume that the pinball is a solid uniform sphere of radius r = 1.0 cm and mass m = 25g. If it is rolling without slipping (Section 10–9) at a speed of 3.0 m/s when it leaves the launcher, what is the spring constant of the spring launcher?
(I) A 1.28-kg mass oscillates according to the equation 𝓍 = 0.650 cos7.40 t where 𝓍 is in meters and t in seconds. Determine the kinetic energy and potential energy when 𝓍 = 0.260 m.
A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute the total mechanical energy of the glider at any point in its motion
A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is at its highest point.