Answer:
(a)The period will increase by 2 times
(b)The period will increase by 2.45 times
Explanation:
(a)[tex]T_{1}=2\pi \sqrt{\frac{m}{k} }[/tex]
When the mass increased by a factor of 4 then;
[tex]T_{2}=2\pi \sqrt{\frac{4m}{k} }[/tex]
[tex]\frac{T_{2} }{T_{1} }=\frac{2\pi \sqrt{\frac{4m}{k} }}{2\pi \sqrt{\frac{m}{k} }}[/tex]
[tex]\frac{T_{2} }{T_{1} }[/tex] =[tex]\sqrt{\frac{4m}{k} } [/tex]× [tex]\sqrt{\frac{k}{m}} [/tex]
[tex]\frac{T_{2} }{T_{1} }=\sqrt{4}[/tex]
[tex]\frac{T_{2} }{T_{1} } =2[/tex]
The period is doubled by 2 times
(b) if the pendulum is taken to the moon where the force of gravitation is about g/6 then
[tex]T_{1}=2\pi \sqrt{\frac{l}{g} }[/tex]
[tex]T_{2}=2\pi \sqrt{\frac{l}{\frac{g}{6} } }[/tex]
[tex]\frac{T_{2} }{T_{1} }=\frac{2\pi \sqrt{\frac{6l}{g} }}{2\pi \sqrt{\frac{g}{l} }}[/tex]
[tex]\frac{T_{2} }{T_{1} }=\sqrt{6}[/tex]
[tex]\frac{T_{2} }{T_{1} }[/tex]=2.45
The period will increase by 2.45 times
