Students set a spring into oscillation with a mass of 50 g and find that it osci
ID: 1400156 • Letter: S
Question
Students set a spring into oscillation with a mass of 50 g and find that it oscillates 50 times in 1 min and 20 seconds. What is the spring constant k in N/m? (a) What is the spring constant k in N/m? (b) Suppose they double the mass to 100 g, and measure 50 oscillations. What is the total time t they measure and what is the corresponding period T ? Students set a spring into oscillation with a mass of 50 g and find that it oscillates 50 times in 1 min and 20 seconds. What is the spring constant k in N/m? (a) What is the spring constant k in N/m? (b) Suppose they double the mass to 100 g, and measure 50 oscillations. What is the total time t they measure and what is the corresponding period T ? Students set a spring into oscillation with a mass of 50 g and find that it oscillates 50 times in 1 min and 20 seconds. What is the spring constant k in N/m? (a) What is the spring constant k in N/m? (b) Suppose they double the mass to 100 g, and measure 50 oscillations. What is the total time t they measure and what is the corresponding period T ?Explanation / Answer
time=1 min 20 seconds=80 seconds
50times in 80 second
1second=50/80=0.625
The frequency of oscillation is the number of full oscillations in one time unit, say in a second.so this will be the frequency
f=0.625hz
w=2*pie*f=2*3.14*0.625
w=3.925rad/sec
k= mw^2
=0.05*(3.9)^2
k=0.77N/m--answer to a
b)1 Hz = 1 oscillation per second
let 50 oscillation are done x seconds
so in 1 second=50/x oscillations
f=50/x
k=mw^2
w=2*3.14*50/x
w=314/x
0.77=0.1*(314)^2/x^2
x^2=0.1*(3.14)^2/0.77
x=113.2seconds
f=50/113.2=0.45hz
T=1/f
=1/0.45
T=2.22 seconds