A 0.45 kg block rests on a frictionless horizontal countertop, where it is attached to a massless spring whose k-value equals 19.0 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until x₁ = -4.00 cm. It then is released from rest and undergoes simple harmonic motion. (a) What is the block's maximum speed (in m/s) after it is released? m/s (b) How fast is the block moving (in m/s) when the spring is momentarily compressed by 1.70 cm (that is, when x = -1.70 cm)? m/s (c) How fast is the block moving (in m/s) whenever the spring is extended by 1.70 cm (that is, when passing through x = +1.70 cm)? m/s (d) Find the magnitude of the displacement (in cm) at which the block moves with one-half of the maximum speed. |x| = cm

A mass of 8.0 kg hangs from a spring attached to the ceiling. The spring has a spring constant of 500 N/m and it stretches 15.7 cm from its mean position. A student grabs the spring, applies a force and stretches it a further 6.7 cm downwards. The block is released and initially accelerates upward before undergoing simple harmonic motion. Calculate the initial vertical acceleration of the mass. (Units: m/s? , to 2 sig figs)

The length of a simple pendulum is 0.85 m and the mass of the particle (the "bob") at the end of the cable is 0.28 kg. The pendulum is pulled away from its equilibrium position by an angle of 6.9° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth. (c) What is the bob's speed as it passes through the lowest point of the swing? O 0

A mathematical pendulum swings with angular amplitude α (α ≪ 1), its period is T . By what factor does the period of the pendulum change if it is suddenly surrounded by two perfectly elastic walls (see figure)? The walls are arranged symmetrically, their angular distance is α.

A vertical spring stretches 8.2 cm when a 1.6 kg block is hung from its end. (a) Calculate the spring constant. This block is then displaced an additional 4.8 cm downward and released from rest. Find the (b) period, (c) frequency, (d) amplitude, and (e) maximum speed of the resulting SHM.

A block is attached to a spring with a sping constant of 7.6 N/m and it undergoes simple harmonic motion.  The amplitude of the blocks motion is 6.30 cm. When the block is halfway between its equilibrium position and the end point of it's motion, its speed is measured to be 28.9 cm/s. Calculate : (a) the mass of the block, (b) the period of the motion, and (c) the maximum acceleration of the block.

A 0.60 kg block rests on a frictionless horizontal surface, where it is attached to a massless spring whose k-value equals 18.5 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until x, = -4.00 cm. It then is released from rest and undergoes simple harmonic motion. (a) What is the block's maximum speed (in m/s) after it is released? 1.23 X Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal). Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which term(s) can be ignored when the spring is compressed and the block at rest? Which term(s) can be ignored when the block is moving at its greatest speed? Use the remaining terms, and the given quantities, to solve for the maximum speed. m/s (b) How fast is the block moving (in m/s) when the spring is…

A lobsterman’s buoy is a solid wooden cylinder of radius r and mass M. It is weighted at one end so that it floats upright in calm seawater, having density ρ. A passing shark tugs on the slack rope mooring the buoy to a lobster trap,pulling the buoy down a distance x from its equilibrium position and releasing it. (a) Show that the buoy will execute simple harmonic motion if the resistive effects of the water are ignored. (b) Determine the period of the oscillations.

An apple weighs 1.04 NN. When you hang it from the end of a long spring of force constant 1.54 N/mN/m and negligible mass, it bounces up and down in SHM. If you stop the bouncing and let the apple swing from side to side through a small angle, the frequency of this simple pendulum is half the bounce frequency. (Because the angle is small, the back and forth swings do not cause any appreciable change in the length of the spring.)   What is the unstretched length of the spring (i.e., without the apple attached)? Express your answer with the appropriate units.

The length of a simple pendulum is 0.75 m and the mass of the particle (the "bob") at the end of the cable is 0.39 kg. The pendulum is pulled away from its equilibrium position by an angle of 8.9° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth. (c) What is the bob's speed as it passes through the lowest point of the swing? (a) Number i 0.58 Units rad/s (b) Number i 0.037 Units (c) Number i 0.435 Units m/s