C.1 Simple harmonic motion HL

Question 1

Phase Angle (ϕ) in SHM

Answer 1

The phase angle in SHM represents the initial angle at time t=0 and is used to determine the starting position of the oscillating object. It’s included in SHM equations as a term (ϕ).

Question 2

Equation for Displacement in SHM

Answer 2

Displacement in SHM can be described by this formula where x_0 is the amplitude, ω is the angular frequency, t is time, and ϕ is the phase angle.

Question 3

Equation for Velocity in SHM

Answer 3

Velocity in SHM is given by this formula, indicating how velocity changes over time, with ω, x_0, and ϕ as angular frequency, amplitude, and phase angle, respectively.

Question 4

Maximum Velocity in SHM

Answer 4

The maximum velocity (v_max) of an object in SHM is ωx_0 where ω is the angular frequency and x_0 is the amplitude.

Question 5

Relationship Between Displacement and Velocity in SHM

Answer 5

n SHM, the velocity is the derivative of displacement with respect to time, leading to a phase difference of π/2 radians (or 90 degrees) between the displacement and velocity waveforms.

Question 6

Total Energy in SHM

Answer 6

The total energy (E_T) in SHM is constant and is given by this formula, where m is mass, ω is angular frequency, and x_0 is amplitude.

Question 7

Maximum Kinetic Energy in SHM

Answer 7

Maximum kinetic energy (E_k) occurs when the object is at the equilibrium position, calculated with this formula

Question 8

Maximum Potential Energy in SHM

Answer 8

Maximum potential energy (E_p) in SHM occurs at the maximum displacement from the equilibrium position and equals the total energy of the system.

Question 9

Energy Transformation in SHM

Answer 9

In SHM, energy continuously transforms between kinetic and potential energy while the total mechanical energy remains constant.

Question 10

Equation for Potential Energy in SHM

Answer 10

Potential energy in SHM is given by this formula, where x is the displacement from equilibrium.