Answer:
a) T= 4.00s
b)T = 5.66s
c)T = 2.83s
d)T = 4.00s
Explanation:
a) The pendulum period is express as
[tex]T_0 = 2\pi \sqrt{\frac{L_0}{g} } = 4.00s[/tex]
The period does not depend on the mass and depend only on the length
so we have,
[tex]T = T_0 = 4.00s[/tex]
b) for new length
[tex]L = 2L_0[/tex]
so, we have
[tex]T_0 = 2\pi \sqrt{\frac{L_0}{g} } = \sqrt{2T_0} = 5.66s[/tex]
c) For a new length
[tex]T_0 = 2\pi \sqrt{\frac{L_0}{g} } = \frac{1}{\sqrt{2} } T_0= 2.83s[/tex]
d) the period does not depend on the amplitude as long as there is simple harmonic motion
so, we have
T = 4.00s
(a) The period is independent of the mass, and the value will remain the same, 4.0s.
(b) When the length is doubled, the period is 5.656s.
(c) When the length is halved, the period of the oscillation is 2.83 s.
(d) The period of the oscillation is independent of the amplitude.
The given parameters;
The relationship between the period and the length of the pendulum is calculated as follows;
[tex]T = 2\pi \sqrt{\frac{l}{g} } \\\\\frac{T_1}{\sqrt{l_1} } = \frac{T_2}{\sqrt{l_2} }\\\\T_2 = T_1 \sqrt{\frac{l_2}{l_1} }[/tex]
(a) The period is independent of the mass, and the value will remain the same, 4.0s.
(b) When the length is doubled, the period is calculated as;
[tex]T_2 = T_1 \sqrt{\frac{l_2}{l_1} }\\\\T_2 = 4.0 \times \sqrt{\frac{2l_1}{l_1} } \\\\T_2 = 5.656 \ s[/tex]
(c) When the length is halved, the period of the oscillation is calculated as follows;
[tex]T_2 = T_1 \sqrt{\frac{l_2}{l_1} }\\\\T_2 = 4.0 \times \sqrt{\frac{l_1}{2l_1} } \\\\T_2 = 2.83 \ s[/tex]
(d) The period of the oscillation is independent of the amplitude.
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