PHY2606
ASSIGNMENT 2
2023
, Solution:
a).
𝐸(𝑡) = 𝐸𝑜 𝑒 −𝑟𝑡
Since the energy of oscillation decreases to one − half its value in about 1 sec, then
𝐸𝑜
𝐸(1) =
2
𝐸𝑜
𝐸𝑜 𝑒 −𝑟(1) =
2
1
𝑒 −𝑟 =
2
1
−𝑟 = ln ( )
2
1
𝑟 = − ln ( )
2
𝑟 = ln(2)
𝜔𝑜
𝑄=
𝑟
∴ 𝜔𝑜 = 2𝜋(256)
2𝜋(256)
𝑄=
ln(2)
𝑄 = 2320
ASSIGNMENT 2
2023
, Solution:
a).
𝐸(𝑡) = 𝐸𝑜 𝑒 −𝑟𝑡
Since the energy of oscillation decreases to one − half its value in about 1 sec, then
𝐸𝑜
𝐸(1) =
2
𝐸𝑜
𝐸𝑜 𝑒 −𝑟(1) =
2
1
𝑒 −𝑟 =
2
1
−𝑟 = ln ( )
2
1
𝑟 = − ln ( )
2
𝑟 = ln(2)
𝜔𝑜
𝑄=
𝑟
∴ 𝜔𝑜 = 2𝜋(256)
2𝜋(256)
𝑄=
ln(2)
𝑄 = 2320
