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.
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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