Answer:
The value is [tex]n = 18.5 \ oscillations[/tex]
Explanation:
From the question we are told that
The mass is [tex]m = 350 \ g = 0.350 \ kg[/tex]
The length is [tex]L = 45 \ cm = 0.45 \ m[/tex]
The angle is [tex]\theta = 4.5^o[/tex]
The damping constant is [tex]b = 0.010 \ kg/s[/tex]
The time taken is [tex]t = 25 \ s[/tex]
Generally the angular frequency of this damped oscillation is mathematically evaluated as
[tex]w = \sqrt{ \frac{ g}{L} + \frac{b^2}{4m^2} }[/tex]
=> [tex]w = \sqrt{ \frac{9.80 }{ 0.45} + \frac{0.010 ^2}{4* 0.350^2} }[/tex]
=> [tex]w = 4.667 \ s^{-1}[/tex]
Generally the period of the oscillation is mathematically represented as
[tex]T = \frac{2 \pi }{w}[/tex]
=> [tex]T = \frac{2 * 3.142 }{ 4.667 }[/tex]
=> [tex]T = 1.35 \ s[/tex]
Generally the number of oscillation is mathematically represented as
[tex]n = \frac{t}{T}[/tex]
=> [tex]n = \frac{25}{1.35}[/tex]
=> [tex]n = 18.5 \ oscillations[/tex]
