Question

An air-track glider attached to a spring oscillates with a period of 1.50 s. At t=0s the glider is 4.40 cm left of the equilibrium position and moving to the right at31.9 cm/s.

What is the phase constant?

Answer 1

Given that spring oscillates with a time period T = 1.5 sω = 2π / 1.5 = 4π / 3
x = A sin(4π t/ 3 + φ )
v = 4 Aπ / 3 cos(4πt / 3 + φ)

- 4.40 cm = A sin(φ )........(1)
31.9 cm /s = 4 Aπ cos(φ) / 3......(2)
- 31.9 / 4.40 cm = 4 π tan(φ) / 3
- 7.25 = 4.18879tan(φ )
On solving φ = - 1.047 rad= -60.3degrees