Questions: The position of a 50 g oscillating mass is given by x(t)=(2.0 cm) cos (10 t-π / 4), where t is in s. If necessary, round your answers to three significant figures. Determine:
Part A
The amplitude.
Express your answer with the appropriate units.
Value
Units
Submit
Request Answer
Part B
The period.
Express your answer with the appropriate units.
Units
Submit
Request Answer
Part C
The spring constant.
Express your answer with the appropriate units.
Transcript text: The position of a 50 g oscillating mass is given by $x(t)=(2.0 \mathrm{~cm}) \cos (10 t-\pi / 4)$, where $t$ is in s . If necessary, round your answers to three significant figures. Determine:
Part A
The amplitude.
Express your answer with the appropriate units.
Value
Units
Submit
Request Answer
Part B
The period.
Express your answer with the appropriate units.
$\square$ Units
Submit
Request:Answer
Part C
The spring constant.
Express your answer with the appropriate units.
Solution
Solution Steps
Step 1: Determine the Amplitude
The amplitude A is the coefficient of the cosine function in the position equation.
Given x(t)=(2.0cm)cos(10t−π/4), the amplitude A is 2.0cm.
Step 2: Determine the Period
The angular frequency ω is given in the cosine function argument.
Given x(t)=(2.0cm)cos(10t−π/4), the angular frequency ω is 10rad/s.
The period T is related to the angular frequency by T=ω2π.
Calculate T: T=102π=0.628s.
Step 3: Determine the Spring Constant
Use the formula for the angular frequency ω=mk.
Rearrange to solve for the spring constant k: k=mω2.