A mass on a spring vibrates in SHM at a frequency of 16.0 Hz and an amplitude of 8.0 cm. If the mass of the object is 0.16 kg, what is the spring constant? Answer in units of N/m.
okay the answer is 1617 N/m but I have no clue how you get that answer! PLEASE HELP
okay the answer is 1617 N/m but I have no clue how you get that answer! PLEASE HELP
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Starting our clock when the mass is at its maximum extension, the position of the mass is:
x = 8 cm * cos(2Ï€ * 16Hz * t)
Taking the derivative twice, the acceleration is:
a = - 2^13 π^2 cos(32π t) cm/s^2
Specifically, the acceleration at t = 0 (maximum extension) is a = -2^13 π^2 cm/s^2
From acceleration we can calculate force and then the spring constant.
k = - ma / x
k = 1617 kg/s^2
x = 8 cm * cos(2Ï€ * 16Hz * t)
Taking the derivative twice, the acceleration is:
a = - 2^13 π^2 cos(32π t) cm/s^2
Specifically, the acceleration at t = 0 (maximum extension) is a = -2^13 π^2 cm/s^2
From acceleration we can calculate force and then the spring constant.
k = - ma / x
k = 1617 kg/s^2