A 300 g ball is thrown horizontally at a speed of 15 m/s and collides with a spring attached to a wall. The ball is in contact with the spring for 0.5 s before bouncing back. Find the spring constant.

A spring-mass oscillator is used in a mechanical clock to be exhibited during the school's science fair. It consists of two springs, with spring constants k₁ and k₂, where k₁=k₂/4, and bob of mass m, as shown below. Derive an expression for the bob’s oscillation frequency f in terms of the frequencies f₁ and f₂ at which it would oscillate if attached to spring 1 or spring 2 alone. 

What is the stiffness constant of the spring that is compressed by 6.0 m when a 960-kg vehicle collides with it at a speed of 26 m/s?

A wooden cube fixed on one end of a perfect spring lies on a horizontal smooth surface where it performs SHM. The motion has an amplitude A. The mass covers the distance +A to -A in 2.64s. The amplitude is doubled to A₁ = 2A, how much time will the cube take when traveling from x₁ = +A₁/4 to x₂ = -A₁/4?

A 1.6 kg block is fixed to one end of a spring. The motion of the block is monitored and the position as a function of time is graphed below. Determine the period and frequency of the oscillation.

An aluminum mass m is placed on a frictionless horizontal surface and connected to two copper wire springs arranged in series. The first spring, made from a thicker gauge of copper wire, has a different spring constant from the second, which is made from a thinner gauge. Determine the period T of horizontal oscillation for the aluminum mass.

A 225 g object placed on a frictionless horizontal table and attached to a spring executes a simple harmonic motion. The spring constant is 125 N/m. The maximum measured displacement from the position of equilibrium is 8 cm. What is the total mechanical energy of the spring object system?

Consider that the oxygen atom in a NO molecule undergoes a simple harmonic motion with a frequency f and an amplitude A. At the equilibrium position, the elastic potential energy of the oxygen atom is set to zero. Find a) i) the displacement and ii) the velocity of the oxygen atom when the kinetic energy and elastic potential energy are equal. b) i) How many times does this happen during a given period? ii) and what is the time interval separating two consecutive occurrences? c) Calculate the percentage of mechanical energy that is kinetic energy when the oxygen atom's displacement is one-third of its maximum displacement. Note that at t = 0, x = A.

A metal ball of 2.43 kg is attached to the free end of an elastic spring, the other end of which is fixed. The ball is pulled from the equilibrium and released which causes it to oscillate. The displacement of the ball from the equilibrium is given by x = 0.430 cos(5.30 t), where the quantities are measured in the SI units. Determine the kinetic and potential energy of the metal ball corresponding to the displacement x = 0.215 m.

The suspension of a vehicle is an assembly of coil springs that keep the vehicle from bouncing too much when riding over an irregular surface. Consider a motorcycle of mass 300 kg with one coil spring on each wheel, and the motorcycle's mass is evenly distributed over the two coils. The two coils are identical and have a spring constant of 5.5 × 10⁵ N/m each. The motorbike transports two 65 kg riders. Calculate the frequency of the oscillations of the motorcycle. Consider the motorcycle in simple harmonic motion.