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.

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.
failed

Solution

failed
failed

Solution Steps

Step 1: Determine the Amplitude
  • The amplitude A A is the coefficient of the cosine function in the position equation.
  • Given x(t)=(2.0cm)cos(10tπ/4) x(t) = (2.0 \, \text{cm}) \cos(10t - \pi/4) , the amplitude A A is 2.0cm 2.0 \, \text{cm} .
Step 2: Determine the Period
  • The angular frequency ω \omega is given in the cosine function argument.
  • Given x(t)=(2.0cm)cos(10tπ/4) x(t) = (2.0 \, \text{cm}) \cos(10t - \pi/4) , the angular frequency ω \omega is 10rad/s 10 \, \text{rad/s} .
  • The period T T is related to the angular frequency by T=2πω T = \frac{2\pi}{\omega} .
  • Calculate T T : T=2π10=0.628s T = \frac{2\pi}{10} = 0.628 \, \text{s} .
Step 3: Determine the Spring Constant
  • Use the formula for the angular frequency ω=km \omega = \sqrt{\frac{k}{m}} .
  • Rearrange to solve for the spring constant k k : k=mω2 k = m\omega^2 .
  • Given mass m=50g=0.050kg m = 50 \, \text{g} = 0.050 \, \text{kg} and ω=10rad/s \omega = 10 \, \text{rad/s} .
  • Calculate k k : k=0.050×(10)2=5.00N/m k = 0.050 \times (10)^2 = 5.00 \, \text{N/m} .

Final Answer

Part A: 2.00cm \boxed{2.00 \, \text{cm}}

Part B: 0.628s \boxed{0.628 \, \text{s}}

Part C: 5.00N/m \boxed{5.00 \, \text{N/m}}

Was this solution helpful?
failed
Unhelpful
failed
Helpful