A simple pendulum, 0.6m long, has a period of 1.5s. What is the period of a similar pendulum of 0.4m length in the same location?

inkytalons

5 years ago

T1 = 1.5s, L1= 0.6m,
T2 = ?, L2 = 0.4m,

From T1/T2 = √L1/√L2....

1.5/T2 = √0.6/√0.4

Divide both sides by "1.5"....

1/T2 = (√0.6/√0.4) ÷1.5

1/T2 = (√0.6/√0.4) × 1/1.5

Then it stands to reason that....

T2 = (√0.4/√0.6) × 1.5

T2 = 1.5(√0.4/√0.6)

Remember that 0.4 is 4/10, and 0.6 is 6/10....

T2 = 1.5[(√4/√10) ÷ (√6/√10)]

T2 = 1.5[(√4/√10) × (√10/√6)]

Two divides 4 and 6, then 10 divides both 10s.

T2 = 1.5[(√2/√3)]s

mosesoghenefejiro

2 years ago

I also wished the answers were left in decimal

ifeagwazi

9 months ago

just imagine

Gunter2023

1 year ago

T1/✓L1=T2/✓L2
T1=1.5, T2=?
L1=✓0.6. Multiply by 10 to remove decimal=10×0.6=✓6
L1=0.4 multiply by 10 to clear decimal 0.4×10=✓4

1.5/✓6=T2/✓4
T2=1.5×✓4/✓6
T2=1.5×✓2/✓3

1.5/✓0.6

Oyiza24

2 years ago

why is the answer not in decimal

Dave333

5 years ago

Answer