91影视

1. Angular frequency of the harmonic oscillator, $蝇=1.20\text{鈥塺补诲}/\text{s}$
2. Vertical axis scale values,$x_s=5.0\text{鈥塩尘}/\text{s}$ and.$v_s=5.0\text{鈥塩尘}/\text{s}$

Using the formula of velocity function and position function, we can find the phase constant of SHM by taking the ratio of velocity and position functions.

Formulae:

The general expression for velocity of motion,$x=x_m\text{cos}(蝇t+f)$ (i)

The general expression for velocity of motion, $v=鈭�x_m蝇\text{sin}(蝇t+f)$ (ii)

Dividing equations(ii) by (i), we get

$\frac{v\left(t\right)}{x\left(t\right)}=鈭�\frac{x_m蝇\text{sin}(蝇t+f)}{x_m\text{cos}(蝇t+f)}$

At
$t=0\text{鈥塻},\text{鈥�}{v}_0=5\text{鈥塩尘}/\text{s},\text{鈥�}{x}_0=5\text{鈥塩尘}$

$\begin{array}{c}\frac{v_0}{x_0}=鈭�蝇\frac{\text{sin}\left(f\right)}{\text{cos}\left(f\right)}\\ \frac{v_0}{鈭�蝇x_0}=\text{tan}f\\ f={\text{tan}}^{鈭�1}\left(\frac{v_0}{鈭�蝇x_0}\right)\\ ={\text{tan}}^{鈭�1}\left[\frac{(5\text{鈥塩尘}/\text{s})}{(鈭�1.20\text{rad}/\text{s})\left(5\text{鈥塩尘}\right)}\right]\\ =鈭�0.695\text{鈥塺补诲}\end{array}$

Therefore,the phase constant of the SHM, if the position functions$\text{x}\left(\text{t}\right)$is in the form

$x\left(t\right)=x_m\text{cos}(蝇t+f)$, is $鈭�0.695\text{鈥塺补诲}$.