Question

An air-track glider attached to a spring oscillates with a period of 1.50 s . at t=0s the glider is 5.10 cm left of the equilibrium position and moving to the right at 37.0 cm/s .what is the phase constant? find the value between −π and π .

Answer 1

To find the phase constant of the oscillating glider, use the equation for simple harmonic motion and the given initial conditions.

Step-by-step explanation:

To find the phase constant of the oscillating glider, we need to use the equation for simple harmonic motion:

x(t) = A cos(ωt + φ)

where x(t) is the displacement of the glider at time t, A is the amplitude, ω is the angular frequency (2π/T), and φ is the phase constant. In this case, we are given the period T = 1.50 s and the initial conditions: x(0) = -5.10 cm and v(0) = 37.0 cm/s to the right.

Using these values, we can solve for the phase constant φ:

φ = arccos((-x(0))/A) - ωt

Substituting the given values, we get: φ = arccos((-(-5.10 cm))/A) - (2π/1.50 s) * 0 s. Now, we can calculate the value of φ using a calculator.

Remember that the value of φ will be between -π and π.