Let's look at the last picture.

• If you want a black background, you need to be careful not to spill light. It's relatively easy to control in a large studio, it's almost impossible in a small room. You need a background which is far away. You could even shoot outside at night if the weather allows it.

• You need some continuous light to show the trajectory. Note that the pendulum spends more time on the extreme than at the bottom of the trajectory because it's standing still at the extremes and fastest at the bottom. That's why the trajectory seems faded. You could put your continuous source of light closer to the bottom to mitigate that effect.

• To show frozen detail on the pendulum, you could manually trigger the flash when the pendulum is at both extremes. The period of the pendulum is constant and only depends on the length of the string, so you could tap your feet to the "rhythm" and pop the flash when needed. Bert Stephani and David Hobby call it BioWizard sync.

So you could try:

• Very dark environment, except for one continuous light close to your pendulum.
• Launch the pendulum.
• ISO 200, f/10, begin 10 second exposure.
• Get the rhythm, pop flash manually once at both extremes.
• Wait for the exposure to finish.
• Try again with different parameters until it looks good to you. No Photoshop needed!

Here's a related example I took a few years ago.

• Long exposure on a tripod
• 1 red LED on the nose of the skateboard
• 1 blue LED on the tail
• 1 slide in the middle to reverse the direction of the skateboard
• 1 manual flash trigger during the slide