12P What is the phase constant for t... [FREE SOLUTION]

Chapter 15: 12P (page 436)

What is the phase constant for the harmonic oscillator with the velocity function $v (t)$ given in Figure if the position function $x (t)$ has the form $x = x_{m} \cos (蝇迟 + 蠒)$ ? The vertical axis scale is set by $v_{s} = 4.0 cm / s$ .

Short Answer

Expert verified

The phase constant for the harmonic oscillator with the velocity function $v (t)$ , if the position function has the form $x (t) = x_{m} \cos (蝇迟 + 蠒)$ , is $- 0.927 rad$ .

Step by step solution

Stating the given data

Vertical axis scale is set by $v_{s} = 4.0 cm / s$ .

Understanding the concept of displacement equation

Using the formula of velocity, we can find the phase constant for the harmonic oscillator from theposition function of form, $x (t) = x_{m} \cos (蝇迟 + 蠒)$ .

Formulae:

The velocity of a body in motion

$v = \frac{d x}{d t}$ (i)

Equation of displacement of the motion

$x (t) = x_{m} \cos (蝇迟 + 蠒)$ (ii)

Calculation of phase constant of the harmonic oscillator

Differentiating equation (ii), we get

$v = - v_{m} \sin (蝇迟 + 蠒)$ (iii)

Using the values $t = 0 s, v_{m} = 5 cm / s, v = 4 cm / s$ in equation (iii), we get

$\begin{array}{rcl} 4 cm / s & = & - 5 cm / s \sin (蝇 (0) + 蠒) \\ 蠒 & = & \sin^{- 1} (\frac{4}{5}) \\ = & - 0.927 rad \end{array}$

Therefore, the phase constant for the harmonic oscillator with the velocity function $v (t)$ , if the position function has the form $x (t) = x_{m} \cos (蝇迟 + 蠒)$ , is $- 0.927 rad$ .

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91影视

What is the phase constant for the harmonic oscillator with the velocity function $v (t)$ given in Figure if the position function $x (t)$ has the form $x = x_{m} \cos (蝇迟 + 蠒)$ ? The vertical axis scale is set by $v_{s} = 4.0 cm / s$ .

Short Answer

Step by step solution

Stating the given data

Understanding the concept of displacement equation

Calculation of phase constant of the harmonic oscillator

One App. One Place for Learning.

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91影视

What is the phase constant for the harmonic oscillator with the velocity functionv(t)given in Figure if the position function x(t)has the form x=xmcos(蝇迟+蠒)? The vertical axis scale is set by vs=4.0cm/s.

Short Answer

Step by step solution

Stating the given data

Understanding the concept of displacement equation

Calculation of phase constant of the harmonic oscillator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

Waves Physics

Nuclear Physics

Physical Quantities And Units

Further Mechanics and Thermal Physics

Oscillations

Study anywhere. Anytime. Across all devices.

What is the phase constant for the harmonic oscillator with the velocity function $v (t)$ given in Figure if the position function $x (t)$ has the form $x = x_{m} \cos (蝇迟 + 蠒)$ ? The vertical axis scale is set by $v_{s} = 4.0 cm / s$ .