Problem 3: An object oscillates with an angular frequency w = 6 rad/s. At t = 0, the object is at xo = 2.5 cm. It is moving with velocity vx0 = 14 cm/s in the positive x-direction. The position of the object can be described through the equation x(t) = A cos(@t + @). Part (a) What is the the phase constant o of the oscillation in radians? (Caution: If you are using the trig functions in the palette below, be careful to adjust the setting between degrees and radians as needed.) sin() cos() tan() 7 8 HOME cotan() asin() acos() E 5 6 atan() acotan() sinh() 1 3 cosh() ODegrees O Radians tanh() cotanh() END vol BACKSPACE CLEAR Submit Hint Feedback I give up! Part (b) Write an equation for the amplitude A of the oscillation in terms of x, and p. Use the phase shift as a system parameter. Part (c) Calculate the value of the amplitude A of the oscillation in cm.
Problem 3: An object oscillates with an angular frequency w = 6 rad/s. At t = 0, the object is at xo = 2.5 cm. It is moving with velocity vx0 = 14 cm/s in the positive x-direction. The position of the object can be described through the equation x(t) = A cos(@t + @). Part (a) What is the the phase constant o of the oscillation in radians? (Caution: If you are using the trig functions in the palette below, be careful to adjust the setting between degrees and radians as needed.) sin() cos() tan() 7 8 HOME cotan() asin() acos() E 5 6 atan() acotan() sinh() 1 3 cosh() ODegrees O Radians tanh() cotanh() END vol BACKSPACE CLEAR Submit Hint Feedback I give up! Part (b) Write an equation for the amplitude A of the oscillation in terms of x, and p. Use the phase shift as a system parameter. Part (c) Calculate the value of the amplitude A of the oscillation in cm.
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![## Problem 3:
An object oscillates with an angular frequency \( \omega = 6 \, \text{rad/s} \). At \( t = 0 \), the object is at \( x_0 = 2.5 \, \text{cm} \). It is moving with velocity \( v_{x0} = 14 \, \text{cm/s} \) in the positive x-direction. The position of the object can be described through the equation \( x(t) = A \cos(\omega t + \phi) \).
### Part (a)
**Question:** What is the phase constant \( \phi \) of the oscillation in radians?
**Instructions:**
- If you are using the trig functions in the palette below, be careful to adjust the setting between degrees and radians as needed.
**Input Field:**
\[ \phi = \]
**Calculator Palette:**
- Trigonometric functions: \( \sin() \), \( \cos() \), \( \tan() \), \( \cotan() \), \( \asin() \), \( \acos() \), \( \atan() \), \( \acotan() \)
- Hyperbolic functions: \( \sinh() \), \( \cosh() \), \( \tanh() \), \( \coth() \)
- Numbers: \( \pi \), \( E \), digits 1 to 9, 0
- Operations: addition (+), subtraction (-), multiplication (\(\times\)), division (\(\div\)), square root (\( \sqrt{} \))
**Options:**
- Degrees
- Radians
**Buttons:**
- Submit
- Hint
- Feedback
- I give up!
### Part (b)
**Question:** Write an equation for the amplitude \( A \) of the oscillation in terms of \( x_0 \) and \( \phi \). Use the phase shift as a system parameter.
### Part (c)
**Question:** Calculate the value of the amplitude \( A \) of the oscillation in cm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16b3faf9-43d0-4d91-9d43-af20944c31b6%2F79593faa-f265-4b6d-8504-f76b7f2be874%2Ff1ms47_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem 3:
An object oscillates with an angular frequency \( \omega = 6 \, \text{rad/s} \). At \( t = 0 \), the object is at \( x_0 = 2.5 \, \text{cm} \). It is moving with velocity \( v_{x0} = 14 \, \text{cm/s} \) in the positive x-direction. The position of the object can be described through the equation \( x(t) = A \cos(\omega t + \phi) \).
### Part (a)
**Question:** What is the phase constant \( \phi \) of the oscillation in radians?
**Instructions:**
- If you are using the trig functions in the palette below, be careful to adjust the setting between degrees and radians as needed.
**Input Field:**
\[ \phi = \]
**Calculator Palette:**
- Trigonometric functions: \( \sin() \), \( \cos() \), \( \tan() \), \( \cotan() \), \( \asin() \), \( \acos() \), \( \atan() \), \( \acotan() \)
- Hyperbolic functions: \( \sinh() \), \( \cosh() \), \( \tanh() \), \( \coth() \)
- Numbers: \( \pi \), \( E \), digits 1 to 9, 0
- Operations: addition (+), subtraction (-), multiplication (\(\times\)), division (\(\div\)), square root (\( \sqrt{} \))
**Options:**
- Degrees
- Radians
**Buttons:**
- Submit
- Hint
- Feedback
- I give up!
### Part (b)
**Question:** Write an equation for the amplitude \( A \) of the oscillation in terms of \( x_0 \) and \( \phi \). Use the phase shift as a system parameter.
### Part (c)
**Question:** Calculate the value of the amplitude \( A \) of the oscillation in cm.
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