An M = 12.3 kg mass is suspended on k = 273000 N/m spring. The mass oscillat up-and-down from the equilibrium positi Yeq = 0 according to y(t) = A sin(wt + $0). Calculate the angular frequency w of t oscillating mass. Answer in units of s 8-¹. At time to = 0 the mass happens to be yo = 19.8 cm and moving upward at veloci v0 = +58.4 m/s. (Mind the units!) Calculate the amplitude A of the oscillati mass.
An M = 12.3 kg mass is suspended on k = 273000 N/m spring. The mass oscillat up-and-down from the equilibrium positi Yeq = 0 according to y(t) = A sin(wt + $0). Calculate the angular frequency w of t oscillating mass. Answer in units of s 8-¹. At time to = 0 the mass happens to be yo = 19.8 cm and moving upward at veloci v0 = +58.4 m/s. (Mind the units!) Calculate the amplitude A of the oscillati mass.
Related questions
Question
![An \( M = 12.3 \, \text{kg} \) mass is suspended on a \( k = 273000 \, \text{N/m} \) spring. The mass oscillates up-and-down from the equilibrium position \( y_{\text{eq}} = 0 \) according to
\[ y(t) = A \sin(\omega t + \phi_0). \]
**Task 1: Angular Frequency**
Calculate the angular frequency \( \omega \) of the oscillating mass.
**Answer in units of** \( \text{s}^{-1}. \)
---
**Task 2: Amplitude**
At time \( t_0 = 0 \) the mass happens to be at \( y_0 = 19.8 \, \text{cm} \) and moving upward at velocity \( v_0 = +58.4 \, \text{m/s}. \) (Mind the units!)
Calculate the amplitude \( A \) of the oscillating mass.
**Answer in units of** \( \text{cm}. \)
---
**Task 3: Initial Phase**
Calculate the initial phase \( \phi_0 \). Answer in range \( 0 \leq \phi_0 < 360^\circ \).
**Answer in units of** \( \text{degrees}. \)
---
**Task 4: Position at Given Time**
Calculate the position of the oscillating mass at the time \( t = 0.0662 \, \text{s}. \)
**Answer in units of** \( \text{cm}. \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7b1f94a-aeb1-4e21-a353-b14674dcbf02%2F063ae8b3-35ea-4b6b-83bb-33320d31f09e%2Fhi7r29u_processed.png&w=3840&q=75)
Transcribed Image Text:An \( M = 12.3 \, \text{kg} \) mass is suspended on a \( k = 273000 \, \text{N/m} \) spring. The mass oscillates up-and-down from the equilibrium position \( y_{\text{eq}} = 0 \) according to
\[ y(t) = A \sin(\omega t + \phi_0). \]
**Task 1: Angular Frequency**
Calculate the angular frequency \( \omega \) of the oscillating mass.
**Answer in units of** \( \text{s}^{-1}. \)
---
**Task 2: Amplitude**
At time \( t_0 = 0 \) the mass happens to be at \( y_0 = 19.8 \, \text{cm} \) and moving upward at velocity \( v_0 = +58.4 \, \text{m/s}. \) (Mind the units!)
Calculate the amplitude \( A \) of the oscillating mass.
**Answer in units of** \( \text{cm}. \)
---
**Task 3: Initial Phase**
Calculate the initial phase \( \phi_0 \). Answer in range \( 0 \leq \phi_0 < 360^\circ \).
**Answer in units of** \( \text{degrees}. \)
---
**Task 4: Position at Given Time**
Calculate the position of the oscillating mass at the time \( t = 0.0662 \, \text{s}. \)
**Answer in units of** \( \text{cm}. \)
Expert Solution
Step 1
Step by step
Solved in 3 steps with 3 images
