a 50kg mass is suspended from a spring, causing it to extend by 30mm. calceolate the spring stiffness?
The mass is then pulled down a distance of 90mm and released. calculate the frequency of the resulting motion, assuming that this is simple harmonic, calculate the velocity of the mass as it reaches a point 20mm below the highest point of its motion? what is its maximum acceleration?
mg = kx = k = mg/x = 50 x 9.81/0.03 = 16350n/m
t= 2pi sqrt m/k = 2pi sqrt 50/16350 = 0.347sec...
calculated the stiffness any help on the other questions?
To calculate the frequency of the resulting motion, you can use the formula:
f = 1 / T
Where f is the frequency and T is the period. The period can be calculated using the equation:
T = 2π√(m/k)
Given that the mass is 50 kg and the stiffness (k) is 16350 N/m, we can plug these values into the equation:
T = 2π√(50/16350)
Calculating this, we find that T is approximately 0.347 seconds.
Next, to find the velocity of the mass when it reaches a point 20mm below the highest point of its motion, we can use the equation:
v = Aω
Where v is the velocity, A is the amplitude (which is the maximum distance from the equilibrium position), and ω is the angular frequency. The angular frequency can be calculated using the equation:
ω = 2πf
Since we know the frequency (0.347 Hz), we can find ω:
ω = 2π(0.347)
Now we can calculate the velocity:
v = Aω
Since the amplitude is given as 20mm (or 0.02m), we have:
v = 0.02 * 2π(0.347)
Calculating this, we find that the velocity is approximately 0.043 m/s.
Finally, to find the maximum acceleration, we know that the maximum acceleration occurs when the mass is at the extreme points of its motion. Using the equation:
a = ω^2A
where a is the acceleration and A is the amplitude, we can calculate:
a = (2π(0.347))^2 * 0.02
Calculating this, we find that the maximum acceleration is approximately 0.758 m/s^2.