# Intro to Simple Harmonic Motion (Horizontal Springs) Practice Problems

An object of mass 1.20 kg is attached to an ideal spring. The object's velocity as a function of time follows the relation v_{x}(t) = -(6.20 cm/s) sin[(7.53 rad/s)t - π/4)]. Calculate the period of the motion and the spring's force constant.

A frictionless trolley of mass 14.2 kg attached to an ideal spring has a velocity function v_{x}(t) = -(8.50cm/s) sin[(5.20 rad/s)t + π/3)]. Determine the i) amplitude and ii) peak acceleration of the trolley.

A block of mass 0.650 kg attached at the end of an ideal horizontal spring undergoes SHM. When x = -0.130 m, its acceleration is 2.80 m/s^{2}. Determine the time taken by the block to complete one oscillation.

SHM is used to determine the mass of objects. One procedure involves attaching a X kg container at the end of a spring. The empty container completes an oscillation in 0.80 s. When a block is placed in the container, the period of the oscillation becomes 1.90 s. Determine the mass of the block.

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 A_{1} = 2A, how much time will the cube take when traveling from x_{1} = +A_{1}/4 to x_{2} = -A_{1}/4?

A plastic disk is fixed to a perfect horizontal spring and placed on a horizontal smooth surface where it oscillates in SHM. The mass travels from -A to +A in 3.42 s. What is the time taken to travel from +A/2 to -A/2 when the amplitude is halved to A/2?

The head of a periodic hammer moves in simple harmonic motion parallel to the x-axis at a frequency of 8.0 Hz. When t = 1.58s, the position of the head is -2.3 cm while its velocity is +20.0 cm/s. Determine the acceleration of the head at t = 1.58s.

A cube of mass 2.60 kg is fixed to one end of a perfect spring of k = 190 N/m and placed on a frictionless surface. When t = 0, the spring has its unstretched length while the cube has a velocity of 5.40 m/s in the negative direction. Determine the amplitude and phase angle. Express your answer in the form of a position-time function.

A crate executes SHM at the end of a spring with an amplitude of 168 cm and a period of 0.419 s. When t = 0, the crate has maximum displacement and is momentarily at rest. What is the time taken by the block to move from i) 168 cm to 62 cm and ii) 62 cm to 0 cm?

There are various methods of determining the spring force constant of a spring. One method involves measuring the mass and oscillation times for the mass. In one setup, you use a mass of 0.820 kg and measure the time it takes the mass to move from a point -A to the next instance it comes back to this same point to be 3.2 s. What is the force constant for the spring?

A spring of unknown force constant has a 3.20 kg block fixed to one of its ends. The block position as a function of time is shown in the graph below. Determine the amplitude of the oscillation and the spring's force constant.

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.

Bees flap their wings at a rate of 13,800 beats/minute. Determine the period (T), the frequency (f), and the angular frequency (ω) for the flapping of a bee's wings.

A sewing needle performs SHM with an amplitude of 2.3 cm and a frequency of 20 Hz. Determine the time taken to move from y = 0 to y = 2.3 cm.

The variation of the displacement with time for a vibrating mass is shown in the graph below. Determine the frequency and angular frequency for the vibration.

The graph below shows displacement as a function of time for a vibrating mass. Determine the period and amplitude of the vibration.

Vibrating objects emit sound that matches their vibrating frequency. In music, this frequency is categorized into notes. A keyboardist is playing C# (C-sharp) note with a frequency of 554 Hz. The sound is emitted by the diaphragm in a speaker that vibrates at this frequency. Determine the time taken by the diaphragm to complete one cycle and its angular frequency.