The mass in kilograms that must be added to the object to change the period to 2.2 s is 1.025kg
The formula for calculating the period of a simple pendulum is expressed as:
[tex]T= 2\pi \sqrt{\frac{m}{k} }[/tex]
m is the mass of the spring
k is the spring constant
Given the following parameters
m = 0.415kg
T = 1.4 secs
Get the spring constant
[tex]1.4=2(3.14)\sqrt{\frac{0.415}{k} } \\1.4=6.28\sqrt{\frac{0.415}{k} }\\ 0.2229=\sqrt{\frac{0.415}{k} }\\ \frac{0.415}{k} =0.0497\\0.0497k=0.415\\k=\frac{0.415}{0.0497}\\k= 8.35N/m[/tex]
Given the period is 2.2secs, the mass of the spring will be expressed as:
[tex]2.2=2 (3.14)\sqrt{\frac{m}{8.35} } \\2.2=6.28\sqrt{\frac{m}{8.35} }\\\sqrt{\frac{m}{8.35} }=0.3503\\\frac{m}{8.35} =0.1227\\m=1.025kg[/tex]
Hence the mass in kilograms that must be added to the object to change the period to 2.2 s is 1.025kg
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