Answer:
The time when the mass will reach its first maximum velocity is 1.8 s.
Explanation:
Given;
mass of the pendulum, m = 3 kg
length of the pendulum, l = 0.8 m
height in which the pendulum is raised to, h = 0.2 m
the mass will reach its first maximum velocity when it returns to its initial position, i.e at the middle (x = 0).
the distance between the initial position of the pendulum and the height in which it is raised is the maximum displacement (A).
If we form a right angle triangle with respect to the height in which the pendulum is raised;
the height of the right triangle, H = L - 0.2 = 0.8 - 0.2 = 0.6 m
the hypotenuse side, = L = 0.8 m
the base of the triangle (opposite side) = A
A² = L² - H²
A² = (0.8)² - (0.6)²
A² = 0.28
A = √0.28
A = 0.529 m
The maximum velocity of the pendulum is calculated as;
[tex]V_{max} = A \omega\\\\V_{max} = A \sqrt{\frac{g}{l} } \\\\V_{max} = (0.529)\sqrt{\frac{9.8}{0.8} }\\\\V_{max} = 1.852 \ m/s[/tex]
The period is calculated as;
[tex]V_{max} = A\omega\\\\V_{max} = A (\frac{2\pi}{T} )\\\\T = \frac{2\pi A }{V_{max}}\\\\T = \frac{2\pi \ \times \ 0.529}{1.852} \\\\T = 1.8 \ s[/tex]
Therefore, the time when the mass will reach its first maximum velocity is 1.8 s.
