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Answer :
Final answer:
The phase constant is 0. The phase at t=0 s is 0, at t=0.5 s is π/3, at t=1.0 s is 2π/3, and at t=1.5 s is 2π.
Explanation:
In this problem, we are given that an air-track glider attached to a spring oscillates with a period of 1.5 s. At t=0 s, the glider is 5.00 cm left of the equilibrium position and moving to the right at 36.3 cm/s.
a. To find the phase constant, we can use the equation: phase = 2π(t/T) + φ, where t is the time, T is the period, and φ is the phase constant.
At t=0 s, the phase is 0, so we can substitute these values into the equation:
0 = 2π(0/1.5) + φ
Simplifying the equation, we get:
0 = 0 + φ
Therefore, the phase constant (φ) is 0.
b. To find the phase at specific times, we can use the same equation: phase = 2π(t/T) + φ.
Substituting the given values into the equation, we can calculate the phase at different times:
At t=0 s:
phase = 2π(0/1.5) + 0 = 0
At t=0.5 s:
phase = 2π(0.5/1.5) + 0 = π/3
At t=1.0 s:
phase = 2π(1.0/1.5) + 0 = 2π/3
At t=1.5 s:
phase = 2π(1.5/1.5) + 0 = 2π
Learn more about phase constant and phase in oscillatory motion here:
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