Answer:
T = 1.46 s
Explanation:
The time period of pendulum can be given as:
[tex]T = 2\pi \sqrt{L/g}[/tex] ------ (1)
Where,
L = Length of String = 52.8 cm
g = gravity = 9.81 m/s2
Substituting the values in equation (1),we get,
[tex]T= 2\pi \sqrt{52.5*10^{-2} /9.81}[/tex]
[tex]T = 1.46 s[/tex]
Notes:
- The time period equation of simple harmonic motion is written as:
[tex]T = 2\pi \sqrt{m/k}[/tex] ------(2)
Where,
m = mass of object
k = Springs constant
The restoring force of pendulum which accelerates the mass towards equilibrium is given as:
mg Sinφ = ks
s = rφ
In this case, r = L
Therefore, s = Lφ
Now,
mg Sinφ = k Lφ
k = mg Sinφ / Lφ
k = (mg/L) (Sinφ/φ)
For all small angles:
lim (φ--->0) = Sinφ/φ = 1
therefore. equation (2) implies:
[tex]T = 2\pi \sqrt{m/mg/L}\\T = 2\pi \sqrt{L/g}[/tex]
In this question: φ = 33°
33° = 33 x π /180
33° = 0.575959 radians
Therefore,
Sin 0.575959 / 0.575959
0.9456
1/0.9456 = 1.057505
Sqrt (1.057505)
1.02835
Now the formula can be written as:
[tex]T = 1.02835* 2\pi \sqrt{L/g}[/tex]
[tex]T = 1.02835 * 2\pi \sqrt{52.8*10^{-2} / 9.81 }[/tex]
[tex]T = 1.50 s[/tex]
So, the accurate answer would be 1.50 s.
