Amplitude is the maximum displacement from equilibrium. the amplitude of the harmonic oscillator after another 20s is about 32 cm.
[tex]A_t=( A_0)e^{\frac t\tau }[/tex].................1
Where,
[tex]A_t[/tex]= 40 cm at 10 s and ? at 20 s
[tex]A_0[/tex] = 60 cm
[tex]t[/tex]= time = 10 and 20 s
First, calculate for [tex]\tau[/tex]
[tex]40= 60 e ^{\frac {10}\tau}\\\\ \dfrac 23 = e ^{\frac {10}\tau}\\\\ln \dfrac 23 = \dfrac {10}\tau}\\\\\tau = 24.66[/tex]
Now, put the value of [tex]\tau[/tex] in equation 1,
[tex]A_ {20s} = 60 e ^{\frac {20}{24.66}}\\\\A _{20s} = 32[/tex]
Therefore, the amplitude of the harmonic oscillator after another 20s is about 32 cm.
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