Question

M (g)	M (kg)	Delta t1(s)	Delta t2(s)	Delta t3(s)	Delta t(s) avg.	T (s)	T2 (s2)
60	0.06	6.53	6.55	6.31	6.46	0.646	0.42
80	0.08	6.63	6.60	6.64	6.62	0.662	0.44
100	0.10	6.99	6.87	7.08	6.98	0.698	0.49
120	0.12	8.12	8.36	8.46	8.31	0.831	0.69
140	0.14	8.35	8.11	8.15	8.20	0.820	0.67

find the slope (4pi^2)/k

calculate the intercept ((4pi^2)/3k)m

Equate the value of the slope found at point 5 with (4pi^2)/k and solve for k.

Calculate the % difference between k and k2 %difference = 2* ((|k-k2|)/k+k2)*100 =

Equate the value of the intercept found with ((4pi^2)/3k)m and solve for the value of m.

This is for Simple Harmonic Motion (Hooke's Law)

Determine the spring constant (k) and the period (T)

Answer 1

For the given data

M (g) M (kg) Dt1(s) Dt2(s) Dt3(s) Dt(s)a T (s) T2 (s2)  

60 0.06 6.53 6.55 6.31 6.46 0.646 0.42

80 0.08 6.63 6.60 6.64 6.62 0.662 0.44

100 0.10 6.99 6.87 7.08 6.98 0.698 0.49

120 0.12 8.12 8.36 8.46 8.31 0.831 0.69

140 0.14 8.35 8.11 8.15 8.20 0.820 0.67

the plot of

M and T^2 is as under

for shm

T = a*sqrt(m/k) ( where a is a constant)

hence

T^2 = a^2*m/k

hence slope of m - T^2 curve is a^2/k

slope = 3.75

hence

from the given data

(4*pi^2)/k = 3.75

intercept from the graph = 0.167 = (4*pi^2*m/3k)

4*pi^2/k = 3.75

k = 10.52757802

from intercept

for point 5

m = 0.14 kg

hence

k2 = 11.03189

%difference

2*((k - k2)/(k + k2))*100 = 4.678333491 %

k = 10.52757802

T = a*sqrt(m/k)

slope = A = a^2/k

T = sqrt(Am)

average tiem period = average(sqrt(Am)) = 0.605965175 s