The period is
P = 2 pi sqrt(k/m)
Use that and the mass to get the spring constant, k.
The total energy of the system is
(1/2) k X^2 = 2.30 J,
where X is the amplitude. .
Knowing that and k, solve for X.
(a) Find the force constant of the spring.
135.81 N/m
(b) Find the amplitude of the motion.
i just need help with what equation i should use. im stumped on this question.
P = 2 pi sqrt(k/m)
Use that and the mass to get the spring constant, k.
The total energy of the system is
(1/2) k X^2 = 2.30 J,
where X is the amplitude. .
Knowing that and k, solve for X.
(a) Force constant (k):
The formula for the period (T) of an object undergoing simple harmonic motion is given by:
T = 2π√(m/k)
where T is the period, m is the mass, and k is the force constant.
To find the force constant, we need to rearrange the formula:
k = (2Ï€)^2(m/T^2)
where T = 0.250 s and m = 215 g. We need to convert the mass from grams to kilograms by dividing it by 1000 (1 kg = 1000 g).
k = (2Ï€)^2(0.215 kg) / (0.250 s)^2
k = 135.81 N/m
Therefore, the force constant of the spring is 135.81 N/m.
(b) Amplitude (A):
The total energy (E) of the system is given by:
E = (1/2)kA^2
where E is the total energy and A is the amplitude of the motion.
To find the amplitude, we can rearrange the formula:
A = √(2E/k)
where E = 2.30 J and k = 135.81 N/m.
A = √(2 * 2.30 J / 135.81 N/m)
A = √(0.0337 m^2)
A = 0.1835 m
Therefore, the amplitude of the motion is 0.1835 m.