Energy in Simple Harmonic Motion Practice Problems

A baby of mass 12 kg is sitting in a baby bouncer. The baby bouncer is suspended in a room with the help of a light elastic cord. The unstretched length of the elastic cord is 2 m. When the baby bounces, she executes a simple vertical motion with an amplitude of 8 cm. The cord has its natural unstretched length at the highest point of motion. The elastic potential energy of the unstretched cord is assumed to be zero, and the lowest point reached by the baby as the reference level. Calculate the i) kinetic energy,  ii) elastic potential energy, and iii) gravitational potential energy at the baby's highest point.

A spring-mass system is used to simulate the motion of the human hamstring. The hamstring executes a simple harmonic with an amplitude of 15 cm and an angular frequency of 6.28 rad/s. Calculate I) i) the maximum magnitude of the acceleration and ii) the speed at the equilibrium position; II) i) the acceleration and ii) speed at the position x=-7.5 cm; III) the time needed to go directly from x=0 cm to x=+7.5 cm IV) Which of the quantities requested previously can be determined using the conservation of mechanical energy?

An object of mass m executes a simple harmonic motion when attached to a spring with a spring constant k. The amplitude of the simple harmonic motion is A. Find the position of the object from the equilibrium position if the kinetic energy is double the potential energy. Express your answer in terms of A.

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?

A simple harmonic oscillator is made up of a 0.25 kg object attached to a spring with a force constant of 100 N/m. The object's maximum position, measured from the equilibrium position, is 5 cm. Calculate the object's speed when its position is -2 cm.

A particle executes simple harmonic motion with an amplitude of 25 cm. As the particle passes through the equilibrium point, its speed is 5 cm/s. Calculate the maximum acceleration of the particle.

The figure below shows the position-time graph of a particle oscillating along a horizontal plane. Find the maximum acceleration of the particle.

The position-time graph of a particle attached to a horizontal spring is shown in the image. What is the object's maximum speed?

Consider a proton that is confined within a one-dimensional harmonic oscillator potential. The oscillator has a spring constant of 1.5 N/m. Determine the energy values corresponding to the first three levels of the proton's energy within this system.